I would like to offer a different path that "should" be cheaper.
Do a search in your area for "alternator/starter rebuild service" to see if you have a business within driving distance. I've been paying to rebuild my gens/starters (and yes, more modern alternators) for one simple reason: What you took off already fits - no need to guess or fiddle with the mounting (there was this one Subaru that listed a replacement alternator at several hundred dollars - I got it rebuilt for $70). The plus side is (again, guessing here) that alternator may have an internal regulator. You did say it was charging, so.....
Bearings, diodes/stators (all those internal parts) can be replaced and your alternator put back into top performance i.e. "New". If not rebuildable they can advise you on what it came out of. Also, most parts stores can identify it as well, i.e. GM, Ford, etc and get you an exact replacement - still sticking to the, "It already fits," mindset.
ADDED (14 Mar 22): I had to come back to this after thinking on it more. I made some more assumptions without really knowing. That can be bad when offering opinions as "advice."
Original 4 cyl jeep engines were designed for generator installation from the factory. Eventually, technology advanced and alternators were installed. To retrofit an alternator into an older engine meant making changes to the mount and to the wiring. Starting with the article on the CJ3B Page:
https://cj3b.info/Alternator.htmlMost of this is covered. There are multiple options on mounts and multiple alternator versions available too.
So, Shark49 back to your dilemma. Does your alternator fit well enough to do its job? Are there upgrades to its mount that would make it better? Are you comfortable with a 3-wire or would you prefer a 1-wire? Internal regulator or external regulator? Fix/repair or just flat out replace?
These kinds of questions are going to depend on where you are and where you want to go. I was determined to keep my generator vs. changing to an alternator so when I changed over to 12V, I had to source a 12V generator/regulator. Members with alternators will need to jump in and offer their opinions.
What many suggest is to get the jeep running and drive it. I can testify that if you choose to restore/rebuild, it can take a lot longer than you can imagine and cost more than you can budget for.
Be careful when purchasing components until you can evaluate it belongs with where you want to go.