I would rent the car on the internet before you leave. It will be cheaper and easier. You might need to pick it up from La Spezia and leave it in Mestre.
In Tuscany I would stop in Lucca for lunch, drive to Florence (2 nights) then Siena, Arezzo (1 night) and Ravenna (1 night) (not Tuscany but beautiful)which will take you to Venice.
I like staying in different hotels every night and love driving. You don't have enough time to spend a lot in each place anyway but this will give you an interesting tour. It will be about 700km but with 3 stops that's not a lot of driving per day.
Can't help with 5 Terre villas...Definitely take the walk (yes all 17km!) round the five towns as it's the best thing about the area.
September should be lovely!

I smiled when I read that you'd like to rent a villa in Cinque Terre, although I know that term is used loosely. There are few, if any, structures that would qualify as a villa but there are lots of apartments for rent. We have rented apartments in Manarola, which is the second most southerly of the five villages. An agency with an excellent selection of accommodations is http://www.arbaspaa.com/ The little agency is owned by someone who grew up there, went to university, and then returned more than a decade ago to start this business. He knows the properties. We found him very helpful and responsive.

You are wise to be looking now. He has a selection of apartments with terraces with sea views but, of course, these are the most popular but deservedly so.

We have rented a car after leaving Cinque Terre with pickup in La Spezia. The car rental agencies are not right at the train station (as they are in many cities) but not far away either. You can reach them by public bus or by taxi or you might even want to walk.

We always rent from AutoEurope because they will match prices of other agencies and most of all, for their free phone number to call back to the states - 24 hours a day - if you need help. Once we changed a reservation and that was very easy to do. Another time, our rental car was broken into in Sicily, and, again, having that 800 number and being able to speak to someone fluent in English was a bonus. When you call AutoEurope, you get to speak to a real person almost immediately. Although you can get a lot of information online, we usually speak to someone at their office before finalizing a rental.

To be forthright, AutoEurope is an affiliate of my website, but it was our favorite before our website existed.

Note you will need an International Driving Permit:
http://www.aaa.com/vacation/idpf.html
Unless you have identified places you want to stop on the way to Venice, I would consider having 5 days in Tuscany with the car and then taking a train to Venice for three days.

I am an avid hiker, but 6 days in CT would be too much for me. There are many attractive towns north and south of CT (see many threads here). I loved the Lerici region and can recommend the place I rented from if you are interested:
http://www.liguriaguide.com/liguria-bed-and-breakfast.html

Yes, you can pick up the car in La Spezia. You don't need to drop the car in Mestre and take the train into Venice. You can drive over the causeway into the edge of Venice, to the Piazzale Roma. A number of car rental companies have offices there.

Six days in the Cinque Terre seems a long time. It doesn't take that long to hike the path between the 5 towns. In a pinch, you can do it in a day. And, as idylicItaly says, the CT towns are very small. Not a lot of villas along there. Maybe look at villa locations just north of the CT, towns like Santa Margherita Ligure (there's a hike over the Portofino peninsula) or Sestri Levante or Levanto. These are all on the coast and on the train line to the CT towns.

I would recommend staying in Manarola in the CT, it is beautiful with great eating options and a few nice bars also.

I would also echo an earlier poster's comments about six days being too much in CT...I am a slow traveller but I think 3-4 is loads to trek, eat, relax and swim a bit.

Lucca would be a logical and beautiful first stop when you leave CT.

Villa and the CT don't go together and a week is much too long there. Consider Santa Maria Logure or Portovenere for a longer stay in that area.