Start with a infinity cloud line A4 or equivalent for your exhaust. Vivosun and Vevor make similar fans for less money or they did, prices fluctuate.
I Power makes some cheap 4" carbon filters that work just fine.
Get a Vivo Sun Aero wave circulating fan or just a cheap clip on for air circulation and you're all set. You might want to get two, you need good air circulation to keep away mold.
You can use cheap can fans for exhaust but they are a little louder.
In my 3 x 3 tent for exhaust I have a 6" can fan mounted directly to a 6" filter. total cost for the two was 70 dollars. Might be overkill for a 2 x 2.
Fans are not a luxury you need good circulation and exhaust to keep the heat down, your grow lights are going to generate a lot of heat.