@iremakakca I personally wouldn't play in any world without mods. The vanilla game doesn't have any cleanup routine for corrupt or stale data, it can produce far too many service sims or vehicles, stuck sims can drain resources... the list goes on. The problems are more pronounced in worlds that have other problems because the game engine can only handle so much at once—a higher baseline load means it takes less extra work (from corruption or the like) to push it over the edge. But even in the most well-made undemanding worlds, you'll come to that edge if you play the same save for long enough.
As far as guides go, this is the standard for how to install mods:
https://modthesims.info/wiki.php?title=Game_Help:Installing_Sims_3_Package_Files/Setup_and_Files
The list of mods I'd recommend is the same one in the thread I linked, basically NRaas ErrorTrap, Overwatch, MasterController, Register, and Traffic, and Traveler as well if your sims ever travel. Other than MC, these mods do their cleanup in the background with no user input and no need to change any settings; MC doesn't do anything at all unless you use it to issue a command. So you won't notice any gameplay changes, just the occasional message from ET or another mod notifying you of some basic cleanup.
All of these mods have been thoroughly tested over a decade, they've been downloaded literally millions of times, and none of them will damage a save, let alone your game overall. The mods themselves are still supported on the NRaas site, so if you do notice any issues, you can get help from the developer or other support staff.
As to whether you're better off abandoning this save, that depends on how much you care about it. You can always save your active household to the in-game bin and place the sims in a new save: they'll keep their skills and money, their relationships with each other, and their careers provided the required rabbitholes are present in the world when the sims are placed. If you don't mind starting their outside relationships from scratch, it's certainly a reasonable option. If it would make you sad to lose the rest of the town, then it's probably worth trying to fix this save.