I know the mikuni carb is top priority but after that does the air filter and exhaust really make the engine breathe better?

Is it worth the money invested to not open up the gear case?

Unless you port the factory heads first, get a good valve job; to are wasting your money on the carb. The next thing is the stock camshaft that limits the most flow IMO as it is low lift, low duration, and very wide LSA. To fully answer your questions, I would have a good set of heads installed before I'd do ANYTHING else.

Heads carb and exhaust made mine run a lot stronger, even had to get a "bigger" prop. 12x10 factory 2 bl was lacking. And even with a hammer, changed from 4350 coils to 4700. Long way from fastest but can hold 30+ with 2 adults, ice chest, and gear.

Heads first... you would probably be disappointed with all that money and not much gains with a mikuni ,,,

Here is my take on it just as the others. Your engine is nothing more than a big air compressor. More air in / more air out = more power.
1) head work, because this is very important on getting the air or "flow" into the cylinders. It also involves valve work which can cause power loss by not being properly seated. Valve springs can also cause issues due to spring tension and cause valve float. Having the heads decked will also increase some horsepower due to compression ratio. You can get some cheap HP and still run pump gas by simply decking.

2) exhaust, because more air in needs to be eliminated. Sure you can port your heads and run a stock exhaust, but it would be negating the port work you just had done, thus not being able to fully utilize the power from the head work. An example would be to run around the block in a nice good jog almost sprint, with your mouth closed and 1 finger in your nostril. no good. Now you don't have to go buy some $500 - $700 exhaust. For the time being, gut your stock exhaust and remove the baffles so that the exhaust will "free flow".

With these two alone, you will see a huge improvement. More air in = more air out.

3) Carb or now and days EFI, this will "enhance" the power because now you will be able to get that extra amount of air/fuel in there to make the extra power. Of course EFI is the latest craze and seems to be doing quite well, a carb is sufficient enough and will suit you needs very well.

4) Cam, this will complete the "power" wanted by allowing the heads to breath in more air and fuel and allow that combustion mixture to escape through the exhaust by how much lift your engine can stand. One thing to remember about cams is different grinds for different applications. Also need to make sure your valve geometry is correct when doing this.

So in a final thought, if your looking to get things done on a budget (which we all do), spend the money on a goos set of heads. I did mine own port work so saved some cash there, the heads are a start. Gut exhaust, you can always buy the "cool looking" exhaust later, piece together a carb kit (can save lots of money and has been done lots of times). You can buy a complete carb kit and they will tell you "all the parts are there", well if you have a little patience, you can piece it out and save some real $$. Then when you engine develelopes a case leak of any other issue and you have to open up the case, then install the cam.

Banded, Exhaust can and will help yes. BUT there is a GTR rig in setx, Stock carb, cam, heads, and STOCK exhaust on a 19' borel hull that runs 35-36. Hell run 32 with a 4 wheeler and another guy aswell. A lot has been emphasized on the exhaust, BUT matching the cam to the exhaust you plan on running helps a lot. Just think about that.