Let's pretend that my budget is $20K. I see 30ft catalina boats in this price range. Most of these were made in the 1980's. A boat with the approx age of 35 yrs old-- sounds kind of worrisome to me. But, you experience sailors, tell me what you think?
If it's been maintained, a 35 year old fiberglass hull is no cause for alarm. I regularly sail on a friend's boat that is 50+ years old. But the hull is the about the only thing on that boat that's original.
It's usually the rig, sails, motor, and any electronics that cause you maintenance issues. A 35 year old motor
might still be usable if it's been well maintained. (I have a 25 year old diesel that's still going, but I've spent more on maintenance than I wish.) But it's hard to know the condition of an older motor short of a mechanical survey and an oil analysis. Both of those cost money, but might be well spent. If you go a little smaller and can use an outboard for power, those are a lot easier to update than re-powering a boat with an aging inboard.
A 35 year old boat is unlikely to still have original sails, but if it does you will want to replace them. There are sources of used sails if you want to save, but you need to inspect them carefully. The condition of the rig will depend on where and how it was sailed, but can be determined by inspection on a survey. Aging electronics are OK until they fail, but then won't be worth repairing. However, you probably don't need much in electronics to sail Lake Pontchartrain (there's nothing to hit but the Causeway bridge), and a basic chartplotter will get you to the Gulf Islands. The rest of that stuff is nice to have, but you can live without it if you have too. (I would get at least a good handheld marine radio, to talk to drawbridges and the tugs in the ICW if you get out of the lake.)
So age is not necessarily the biggest issue -- it's how well the boat was maintained, and how much you have left in the budget for updates after you get the boat.
A related thought: There are a lot of Catalina's out there (I have one of over 1,100 Catalina 320s that were sold). Many of them have owners associations that can give you information about issues specific to that model that you might not otherwise know to check. So check out those websites and Facebook groups to get more information about the Catalina 30 or any other model you consider.
As far as whether it's worth it: there is no economic argument for owning a sailboat. But if it literally "floats your boat" then it certainly can be more than worth it.