I’ve been to Paris; the other are on my ‘to do list’.
IMPO you should be aiming for a bare minimum of 3 nights in each place; and I personally would be looking at 4-5 nights as a) you need to factor in travel between destinations, which will cut down your time in the actual place and b) these are all cities with A LOT to see; I’ve been to Paris twice, and still not seen loads of things.
Re hotels: be super-careful, and check the location very carefully before you book. Some hotels billed as being ‘in’ Rome/Paris etc can actually be on the outskirts of the city, and a 30-60 minute commute from the main tourist attractions. If the price seems cheap, this is probably why.
Re budget: I can’t help with flights and so on as I’m from the UK; but in terms of spending money, these are all very expensive cities. I was last in Paris in 2008, and boy is it expensive! There is just nowhere cheap there, and I would be budgeting a minimum of $100 per person per day for food, drinks, entry to attractions etc; as a guide, cocktails start at around $12, beer at around $10, and wine at around $8 (for a large glass). A simple baguette will cost around $9 to take-away; if you eat in, expect to pay more. Dinners start at around $30 for a very basic meal excluding drinks, with the sky the limit. So yeah, not cheap. Venice, Rome and Florence are also expensive, and again, I would be looking to budget a similar amount if you really want to enjoy yourselves and not be constantly worrying about running out of money.
Hotels in any of these destinations start at around $100 per room per night room only for a 3* hotel, if you get a good deal; but you can easily pay 3 or 4 times that amount; it really depends on what you want.
For flights from Italy to Paris, Ryan Air and Easy Jet are the cheapest airlines to fly with, but the baggage allowance is not massive (British Airways is more generous, and about twice the price). A flight from Paris to Italy (or vice versa) starts from around $45 pp one way with Easy Jet or Ryan Air.
Re tour vs site seeing on your own: I personally would never bother with a guided tour in any of these destinations. Going on your own gives you flexibility, so you can see what you want, at your leisure. I like being able to stop at a pretty cafe if I want, without being bundled onto the next attraction. All four cities are easy to navigate; Paris has an excellent tube system which is reasonably priced and easy to nagivate. I would suggest investing in some guide books, and planning your itinerary in advance; sites can be spread out, so it’s worth focusing on one area each day. I’d be happy to make recommendations and suggestions for Paris if you like; I also have a great 1 night 2 day itinerary which takes in several of the main attractions (Notre Dame; Saint Chapelle; Berthillons ice-cream parlour on the Ile Saint Louis (a MUST); the Sacre Coeur; a food market; the Eiffel Tower; a cruise on the River Seine; the Champs Elysses; the Arc du Triomphe)
Hope that helps!