First off, good decision to buy the Ferrari you can afford now, instead of waiting for the one you can't yet - you never know what is going to be around the corner, so enjoy Ferrari driving while you can.
My experience of owing Ferraris is limited to my 550, so I cannot advise you from personal experience on your choice between 348 and 355; and I live in the UK, not the USA, so my knowledge of prices relates to the UK market, not yours. However, from what I see and read, I would conclude that:
1. The 355 is the better car by a margin greater than the apparent similarities would at first sight suggest.
2. It is also the most aesthetically pleasing.
3. Probably because of the above, 355 prices are considerably higher than those for 348s, so you should be able to get a better 348 than a 355 for the same money. This may be particularly significant if your budget won't stretch to a 355 in the condition that you would want.
4. Going only on the basis of age and the fact that newer models are generally less easy for the DIY owner than older ones, I would imagine that you would be able to do more work yourself on a 348 than a 355.
I hope these thoughts are of some help.