The best way to keep your room cool is to get a cool tube and vent it. If you can't afford one, you can make one of your own pretty cheaply
https://www.rollitup.org/do-yourself/161300-batwing-reflector-cool-tube-40-a.html
If you build one and vent it, then you wont need a fan for your intake. It's called a passive intake, just provide the hole and the air venting from the cool tube will create a vacuum that pulls air through the passive intake.
I have a portable A/C too, and the problem with it venting the hot air is that it's not where the hot air is. Heat rises, so unless you're going to mount you're portable A/C up high, it's going to be pulling cooler air to vent. It has to vent the heat from it's coils though, so the air will come out extremely hot.
With the cool tube, a passive intake & portable A/C you should have no heat problems.
You can of course hook up a carbon filter to your exhaust, or you can make one yourself. Check the DIY threads for home made versions. You should really save your money for your fans, it's the only thing I can think of that you can't make yourself for less money. And a good one will cost you upwards of $100. You can find good deals here
http://htgsupply.com/productsubcategories.asp?categoryID=7 Just keep in mind when mounting them that it's easier to push air than it is to pull air. So the fans will do more at the start of the exhaust then at the end of the exhaust.
Be sure to put filters on all of your intakes & exhausts or you'll be vunerable to bugs. Stockings will work on most of your intakes & exhausts until you can get yourself some no-thrip screens. However, you're A/Cs exhaust will probably be too hot for stockings, it will melt them. For that exhaust I suggest either a 3M allergy filter rated at 150 microns, a stove exhaust filter rated at 150 microns, or one of those cone auto air filters. The holes in the cone auto air filters are bigger than 150 microns, but you have to treat the filter with oil that will trap anything that tries to crawl across it. It wont protect against gnats or white flies, but it will protect against mites, aphids, and non flying thrips.
Hope that helps. Good luck