I doubt you'd find anything with an Abarth label for that money, but a replica would be cool. You can pick up the 600 based cars that have been converted into Abarths, some very authentic even. The biggest problem with Abarths is determining what's orginal and what isn't in the Fiat based ones. You'd never find something like a Record Monza for that money. Even with a replica, you're probably not likely to see one at any car show, and only a few vintage racing. They're awesome drivers, and with a one liter, very, very quick.
OK, back to the Alfa suggestion area. A 105 series Bertone GTV would be my top choice, followed by an earlier Sprint, etc. Early spiders that are decent may be above that amount. If you want an early spider, but still affordable, the '74's are nice cars, and for Fiats, I like the 124 Coupes a lot, but look for a good one, but they can be hard to find in any condition. One of my favorite Fiats is still the X1/9, although you may find it a bit common. It's so far ahead of the British cars in driving dynamics its not even funny (I still love my British cars though). With a few mods, it's seriously quick. Nothing this side of a Lotus drives like one. Also already mentioned, the Fiat Racers are really cool, but all but extinct. I still kick myself for passing on one a few years back for only a few hundred dollars, totally rust free but needing paint.
For a nice driver a little newer, Alfa GTV6s are wonderful cars, but still underpriced and mechanically ignored by many that can barely afford them. Awesome sounding motor and nice long distance tourer.
Others to look for: I've seen a few OSCA versions of the Fiat 1200/1500s go for too cheap lately, even if they did need a little work, and I've always wanted a Multipla, a tiny mini van based on the Fiat 600.
Fiat Dinos are also cool, but remember, the motors are more or less the same ones in the Dino 206/246 cars, so expect Ferrari money for rebuild parts, and labor rates if you don't so the work yourself. But they sound like, well a Ferrari, and almost as good as a GTV6!