Well based on what I see there you got a good deal on that oddy.
Goddamn those look like the original tires. Good fender too.
A couple of things to start that I would check and do.
1) That's an air cooled machine so MAKE SURE you run good octane fuel or its all over. Guaranteed.
2) Verify fuel flow rate of the fuel pump. You need 4.5oz in 10sec approx. This is a must do item. Remove the fuel line from the carb and put it into a measuring container with marked ounce measurements. Turn it over with starter and time with a stop watch.
3) Make sure your tank is not rusty inside and that pickup line screens look clean (if they're even still on it)
4) Take a compression test and let us know what it is.
5) The rear suspension on an oddy is non existent. The springs are WAY to stiff. You need to get some 155lb approx. springs. If you don't you will for sure feel it in your back soon.
6) If you have some spare cash and can get a liquid cooled head then go for it. Honda had issues with over heating and had several recalls on the FL350. If your serial number has an X at the end of it then it has been in for some recall repairs.
7) Fix that ding dong hanging out the back of the exhaust. When you roll it or back into something then it will be taken care of for you.
8) Put a filter sock or two on that foam filter. Your
Engine will live longer if you ride in sand. Better yet get the top to that air box.