6 full days in Italy.

Based on my experience, here are my suggestions:
Venice - buy a 24 hr ticket for the water buses (Vaporetto) and visit some of the islands esp Murano and Burano
Florence - take a bus tour to Fiesoli and have lunch there; just walk around the Piazza della Signoria and visit museums and the Duomo: piazza Michelangelo will give you a view of Florence; Bridge of Ponte Vecchio has boutique jewelers and artisan shops. I myself would go back to Firenze and stay a week.
Rome - a lot of walking to see sights. You can just pay for a self- guided tour esp in the Colosseum with audio guides. Do a lot of reading about the city before getting there because there are just too many places to visit. If you want to go to the Borghese gardens, you have to make a reservation.
Enjoy Italy!!

>Is this a reasonable itinerary?
It's do-able as long as you accept you can only scratch the surface of those 3 wonderful cities. Italian trains are safe and comfortable enough.
>Should we start with Venice or Rome given the days of the week we are there?

Makes no difference imo. Many Italian museums, galleries & sights are closed on Mondays but that applies across the country.
Both cities have airports which are fairly near the centre and easily accessible by public transport.
>Should we use guides given our limited time?
That's entirely up to you. Personally, I wouldn't and didn't when making my first visit to those 3 cities (I've visited them all several times). They all have historical centres which are very walkable and safe and all have safe and easy-to-use public transport systems. Venice has vaporetti (boat 'buses'), Metropolitan City of Florence has buses and Rome has an excellent system of Metro, trams and bus.
>What should we prioritise in each place?
Priorities always vary according to personal interest, preferences and budget. I'd suggest:
Venice:  The city's main 'sight' is itself so just walk and walk and walk....don't worry about getting lost! St Mark's Basilica is essential imo, most people want to see the Rialto Bridge and taking a vaporetto along the Canale Grande (Grand Canal) will allow you to see lots of the city's wonderful Medieval architecture. Make sure you go into at least a couple of the many ancient churches: all are full of atmosphere, wonderful architecture & artwork.
Try to find time to explore the less-tourist-visited areas such as Dorsoduro, Cannaregio or Castello. There are very few Venetian residents nowadays but those are the areas where you're most likely to see ordinary day-to-day life (e.g. rubbish collection, postal delivery, non-touristy cafe bars etc etc).
Florence: Walk and walk and walk. The city's historical centre is small, compact and flat. People who are into art often prioritise the Uffizi and/or the Accademia. I'd prioritise the Duomo, Campanile and Baptistry, the Ponte Vecchio, Piazza Della Signoria and as many churches as possible (again, full of atmosphere, architecture & art). Some people like to visit Mercato Centrale and Mercato Nuovo but I've long found both to be overpriced, mostly aimed at tourists and very attractive to pickpockets & scammers.
Rome: Walk and walk and walk.Two weeks wouldn't begin to scratch the surface of this wonderful city. Imo the Colosseum (just from the outside is fine for a short first visit), the Forum and St Peter's Basilica are absolutely essential. NB The only way to see the Sistine Chapel (along with a big crowd of other people) is to visit the Vatican Museums though visiting them will take a minimum of several hours. To that list I'd add any ancient church you pass (atmophere, architecture & artwork again) but most especially the stunning Basilica Santa Maria Maggiore, the Pantheon and the Capitoline Museums.
Many people visit the Spanish Steps and the Trevi Fountain but I'm afraid neither do much for me, especially as both are almost always crowded with loads of tourists.
> Anything we should be aware of
1. Eating and drinking outside will always be more expensive than eating or drinking inside. That's part of Italian culture: it's not just a tourist rip-off.
Don't eat anywhere which hasn't got a menu with prices in its window and/or on the outside tables.
Avoid eating or drinking anywhere along the main tourist routes/near the main sights & sights and anywhere which is obviously aimed at tourists. Explore side-streets to find better food at better prices.

2. The main risk in all European cities is pickpocketing and petty theft rather than anything worse. Many pickpockets/petty thieves are as skilful as the best table magicians but it's pretty easy not to give them an opportunity.
Stay alert, especially when using ATMs. Getting your PIN before pickpocketing your card is very useful! Check who's nearby and if you feel uncomfortable go somewhere else.
Keep your passport, all cards and most money either under your clothing or in the hotel safe. Don't flash cash or wear expensive flashy jewellery/watches. Always wear bags with the strap across your body. Don't keep valuables in bum-bag/fanny-pack or day pack (both are very easy to steal from). 
Be conscious of where you use your phone and where you leave it (on top of a cafe table is *really* not a good idea!). Don't hang your bag on the back of a chair: keep it on your lap or put it on the floor underneath the table and wrap the strap round your foot.
Be on your guard against distraction techniques & scams e.g. someone tells you there is a mark on your back and 'helps' you get rid of it while an accomplice picks your pocket/backpack/bum-bag, someone offers to 'help' with your bags then demands substantial payment, someone shows you a ring they've just 'found' and his/her mates pickpocket you..... Remember you don't have to stop and talk to someone: you can just keep walking. Practice how to say 'No, grazie' politely but firmly. 

This is a very short time to cover even one of these three cities. Even so, you don't need to use guides imo. Just decide exactly what you want to see in each city, bearing in mind you will only be able to cover the absolute highlights of each. So for Venice, you will want to see St Marks Basilica and the Doges Palace; take a Vaporetto from Piazzale Roma to San Marco to see the grand canal; take a Vaporetto from San Marco to San Giorgio Maggiore and visit the church and bell tower. Stellar views of the Doges Palace, the Csmpanile and St Marks Basilica from here. Book Doges Palace tickets in advance. You might consider an evening 'after hours' tour of St Marks Basilica for your first evening; these are expensive but very much worth the money in my opinion. To visit the basilica with no more than around 40 people, rather than the hundreds during the day, is an amazing experience.You might like to spend your second evening in Canareggio, lots of bars and restaurants and picturesque little canals and bridges. Florence highlights are the Duomo, the Baptistry, Piazza Della Signoria, Basilica of Santa Croce, the Palazzo Vecchio, Uffizi Gallery. You won't have time for everything so you must choose! If you want the Uffizi, you must book ahead. For amazing views of the Florence skyline, visit Piazzale Michelangelo at sunset. If you are interested in renaissance art, I highly recommend the Brancacci Chapel. It's very special. There are lots of suggestions online for 48 hour Rome itineraries. I would use day one to cover 'ancient' Rome - the Colosseum, the Forum, the Arch of Constantine. Also on day one you could see the Jewish Quarter and the Pantheon. Book Colosseum tickets well ahead of time.
On day two, you could see the Vatican museum and St Peter's Basilica. I can recommend an early morning Vatican Museum tour - look for one that offers the Sistine Chapel before opening. You will see the chapel with about 100 others, rather then the usual 400 or so!I highly recommend the Borghese Gallery. Book well ahead as they limit the number of daily tickets. From there you can easily walk to Pincio gardens where there is a terrace with panoramic views of Rome. Walk about fifteen minutes to see the Trevi Fountain, then from there it's about a ten minute walk to the Spanish Steps. You could do the Borghese Gallery, Pincio, Trevi and Spanish Steps in the afternoon/evening of the day you arrive in Rome, which would free up time on day two to see other sights or take things at a more relaxed pace. you will need your walking legs as all of these cities are best seen on foot.

It's not a bad way to break up six days, and Venice is a good place to start. You won't really do any of these cities justice, but I think you already know that, so just enjoy yourselves.
One note: When you get to Rome, you're going to assume going down into the Forum is mandatory. DON'T. It's nice and historic, but you can see it from above, from the surrounding streets. Going down into the Forum isn't worth the (sometimes extreme) hassle and expense. By far the better experience is Ostia Antica, the ancient port city that use to serve Rome. It's a ruin now, of course, but it's magnificent and nowhere nearly as crowded as the ancient sites in central Rome. You take the B line on the Metro from Termini station to Basilica San Paolo station. You transfer there to a commuter train, the FC2, from Basilica San Paolo station to Ostia Antica station. The whole trip takes less than an hour. The fare is €1.50. Ostia goes on forever -- you can easily lose yourself there for an entire day. But if you have time, get back on the FC2, go two stops to Ostia Lido Io, and enjoy some beach time. It's clean and lovely.