For $1000 its kinda limited tho'. You'd end up spending a lot more just to restore/upgrade them. If i were you i'd definately get an 86' Corolla Hatchback "Hachi Roku"....it'd be a fun beater car. But these cars are hard to find at around that price.
I recently found two 86' corollas hatch back and a coupe around my area. Got both of them for $500. They were just sitting around as junk cars....so sad. This will be my spring project ...I'll probably switch all the good parts to the hatch and then rebuild from there.
But Other project cars that come to mind are...1st gen MR2, 1st gen DSM Eclipse with 4G63, Old school starlet, early 90s 240sx, Late 80s 300zx Turbo.....no I dont wanna say it.......91 Civic hatchback

Its up to you man.
To find some them you gotta get lucky...they're probably just sitting in someones garage lonely and sad. If anything I wanna get those 60s or 70s Celicas....They have circle headlights and look like muscle cars with big tires. That'd be sweeet.