I would have no problem picking up a car in La Spezia as opposed to Pisa. It's more driving but train from CT village to Pisa probably means a few changes unless you catch an IC, airport tram etc. Plus you have to get from the airport station to the rental car pick up. I am not familiar with Pisa airport don't know how much of a hassle that would be. I definitely would not want to get a car air Pisa rail station. I researched that once and IIRC it just seemed like a driving nightmare to get out of there safely.
I hope Roberto comes along with his advice.
I would get the car in La Spezia. There must be more than Europcar- check with AutoEurope.com.
(not that there is anything wrong with Europcar)
If you are planning to stop along the way to your Tuscany location just be careful of luggage in car. Make sure it is all hidden before you park.