Replacing a worn out engine is the cheapest route.
Upgrading a worn out 3.8 with a 4.1 stroker would be a comparatively cheap option. It would give you "a little bit more" without breaking the bank because it's basically a bolt-in option. No major work required.
A supercharger kit is an option that doesn't break the bank but it's hit-and-miss when it comes to working out well.
Then there's a big gap in cost.
Above that gap is a full on engine swap. No matter what engine you go with, you're going to have to do a ton of fabrication or buy a ton of kit parts to bolt in. If you're not planning $15K+ for an engine swap, you're not swapping an engine in a JK. And you'd be better off with $20K+ in budget.
As it turns out, the 3.6 Pentastar is just about as expensive to swap in as any small block V8. Sure, you can buy parts that will work. But you're buying a ton of new parts that changed when Jeep started putting that V6 in the JK. And when you're done, the Pentastar isn't a huge improvement over the 3.8. Sure, it's "better" but the gains are marginal. You're not going to notice a huge difference between the two. Not enough to make the swap worth it.
Best option if you're going to swap engines is the GM LS V8 family of engines. It's a known quantity. All of the conversion parts are readily available. It's a straightforward swap with not a lot of surprises. But it's not cheap. The desire to keep it a manual transmission will complicate things slightly because that's uncommon to do. But it can be done easily enough.
Second best candidate is the 5.7 Hemi. The Hemi aftermarket is nowhere near the size of GM's aftermarket. So options are a little more limited. The cost is probably on par with a GM LS swap. But the manual transmission options are even more rare.
Ford V8 swaps can be done. But they're really rare. You'll have to do a lot of custom fabrication to make it work. And the cost will be higher. But it can be done. The Nissan and Toyota V8 swaps are probably even more rare and more difficult.
