Do you mean $200-$400 for both together or $200-$400 for each? There are several entry level guns in the $200-$400 range while a basic entry level wireless is going to run you a bit over $500 per channel for anything worth having. Don't forget the other components in your kit that will be necessary to capture good sound - mixer and/or recorder, boom, wind protection (yes, even indoors), proper monitoring headphones, etc. (In-camera recording isn't going to cut it shooting on a DSLR.) And why do you think a shotgun is the way to go in a gymnasium?
I've seen some used Sennheiser Evolution G2 transmitters/receivers selling on forums and on eBay for around $300. That should include the ME2 lav mic which is decent. Gymnasium's are one of the worst possible places to record audio, because of the echos.
If you really want a shotgun and you're going to mount it on camera, just get the Rode videomic. You should be able to stay close to budget and buy both items used
Your requirements (at least as much as you have posted here) seem completely unrealistic.
Strongly suggest that you read all the "sticky" items at the top of the page, and then re-think what you are trying to do.
Recording audio on your DSLR seems ill-advised.
Using a shotgun microphone in a gymnasium is almost always a bad choice. If there is something about your particular situation that exempts you from the laws of physics, you should probably reveal the details here.
Your proposed budget is too low by half just for a decent wireless mic. Why do you think need a wireless mic? If you revealed where you are on the planet (complete the user profile to at least add your country), there may be other things you could do to get decent wireless equipment at lower cost, etc.
If you want to take two steps back and explain WHAT you are trying to do and what your constraints are, we can help you think of more realistic solutions to your situation. But you question as it stands is not really answerable.