Welcome!
I'd say, maybe. You didn't mention your location. There are jeeps to be had. Fully restored can be advertised for more than your budget and projects in varying degrees of completeness can come in a large spread for the asking amount. Posting where you are, may produce an offer close by.
Some here will advertise the need to sell and they'd be in great shape, timing plays a part.
It sounds like the interior dimensions will be a factor. Military and CJ-2A jeeps have a little less leg room. The 3As and 3Bs have a bit more leg room (the wheel wells were shortened and the seats pushed back, I think I remember 2 inches). I think the early CJ-5 has the same leg room (I read the 3A/3B seat frames are the same as in the CJ-5.
Finding a rebuilt/reliable driver will be the challenge - the more time you have, the better chances of finding what you want. Changing your level of "current condition" can also affect options.
There are multiple places to check.
Here, in the Classified Ads section. See what has been posted and even add your Want To Buy ad.
(I counted 5 jeeps advertised for sale since 2023).
eWillys (offline for maintenance right now - good location to filter for the model)
https://www.ewillys.com/I remember reading multiple Facebook sites hosting jeep sales.
Also, Oldtime who's posted here often has advertised his 3B
https://www.thecj2apage.com/forums/1953-cj3b_topic55244.htmlas of May 2026, it was still available. I think it's in Missouri.
Good luck!