I've had an '87 328 for about a year now as a first Ferrari. If you subtract the cost of a discretionary front bumper respray, costs have been about $500 so far this year, including a new battery. I did spend $4K on a major service, water pump rebuild and fuel line replacement when I bought the car.
The car has developed a slight oil drip from around the pan, so I suspect my annual fluid service (normally $200 or so) will be higher because of that.
There are a couple of great independent Ferrari techs near me, so no need to go the dealer. As posted above, these cars are nicely low-tech and well-known by now.
I'll echo the opinions here, that if you want a reasonably reliable Ferrari that won't maul your wallet the 328 is the place to be. Much better electricals than the 308, and without the expensive problems of the 348/355.
While the 328's are old cars now, many have had aged components updated already (mine had a new clutch, new starter, new radiator, new brake lines, etc. by the time I got it.) The 348/355 are also rapidly becoming old cars and will be due for all of that anyway and, at least on the 355, you can spend many thousands of dollars putting things right. Remember, 355s are pushing 10 years old now.
I'm a huge fan of the 355's looks and performance, but ultimately the costs/thrills equation didn't do it for me. A friend just sold his because he was tired of living in fear of Something Big going wrong.
348 prices, except for some late models, seem to have settled at or below 328 levels. You get a lot of car for your money, but spend more keeping it on the road. The looks are love-it-or-hate-it. I happen to like them, but the market opinion isn't overly favorable.
I think we're in a good spot right now, with enough nice 308s and 328s left to get into Ferrari ownership without committing financial suicide. I'd guess that will change as the 308/328s rise in price and become scarcer through attrition.
If you want modern, maybe start with a 328 and wait for 360s to drop even more. There are tons of them for sale now, and they may be under $100K by spring, and I've heard good things about the quality/costs with regard to that model.
If you're not keen on the 308/328 look, obviously don't buy. But anything older than a 360 is an old car.