I have about 200 hours PIC in the 310R and 340A a long time back.
The 310R is a wonderful plane, if budget flying is not your primary interest. The undercarriage is a bit fussy, so don't scrimp on the maintenace dollar there. While it is up on jacks one day, with proper training, and maintenance staff supevision, do a manual gear extension, so you understand how it happens, and confirm that it works properly for yourself.
The fuel system, particularly if wing locker tanks are fitted, is superb, but get competant training on type and on the fuel system specifically. There is a very definate logic flow in using it correctly. I used to cruise at 180kts all day long, but a bit hard on fuel.
The loading is important. Actually do the weight and balance before you fly, particularly if you plan to carry something in the nose baggage compartment.
It's a slippery wing, fast, but not a STOL plane. If you want STOL go Aztec instead. The split flap is good for drag but useless for high lift.
Familarize yourself on the recent airframe maintenance requirements. I am not familiar with thier application to a 310, but they are extensive for some Cessna twins.
The big Continental engines are wonderful, but do have their operating quirks. Get training on them. Starters, and alternator drives are a problem if the engine is not operated and maintained well.
Read "Cessna, Wings for the World II" by Thompson. I just re-read it, and it is an excellent dissertation on the 300 series Cessna twins, by a former Cessna test pilot. It contains a lot of detail on the 310 series, and why they are the way they are.
I'm sure that more will come to my mind, recalling this delightful aircraft.
If you're going to fly this type, get training form a pilot with hundreds of hours on type. A Piper or other light twin type pilot (no 310 time) will not possess the knowledge and experience on type that you will need to operate safely and economically. A Cessna 340 or 400 piston series pilot would be able to help you through ok.
Good luck, Pilot DAR