With a budget of $3-3.5k, you might have more luck going TAG. Trust me, they’re still plenty fast.
If you keep your eyes open, there are good deals on quality used shifters that pop up from time-to-time. Generally, in the $3-3.5k range, you’ll be getting a quality, proven used Stock Honda CR125 (engine only) that was prepared by Swedetech or a big name like that. Go without the big name builder, and the prices tend to come down quite a bit, in which case you might find a complete (kart and engine) package within your budget. The downside to used Stock Honda’s is that they are in demand, so it’s more of a seller’s market than a buyer’s market. If it’s just for playing, a Euro KZ/ICC (pure kart engines) complete (kart and engine) package can probably be found in that price range too. The downside to these engines is there’s not a lot of places to RACE them anymore, which helps a buyer because demand is low.
The best advice about what specifically to look for, which you’ll hear from almost everyone, is to see what is supported locally. This is especially true for someone new to the sport. If you’ve been kart racing for a while, it’s maybe not so important, but for you, you’ll want the support (whether you realize it right now or not).
Opinions differ on whether you should start in a 125 shifter – it’s not so much how fast they are, but it’s how many things you need to process very quickly, and that makes the learning curve of karting that much steeper. Your Vette and Z-car will feel like things happen in slow motion in comparison. Go with a 125 shifter if you want, but given your budget, you might be better off and equally satisfied with a TAG.
The one thing I’d personally avoid, through experience, is buying an older kart package that’s cheap because by the time you fix what needs fixing, you’ve generally spent as much as you would for a quality newer, lightly used kart. And yours is still old and well-used.