I own and have only used the TEMPTU S-One compressor along with their SP-35 gravity feed airbrush gun. (I'm pretty sure its the same as the Sparmax compressor and gun on the OCC site.) Been very happy with it and its definitey within your budget, and you'd probably have enough left over to buy a foundation starter set They also have a PRO program as well which will also save you $$!
In terms of your other questions, you CAN mix makeup brands with different guns, thats not a problem. Just remember to clean your gun well in between using different TYPES of foundations (water based, silicone based, etc), or have a second gun if you need to be constantly switching between foundation types.
I believe you CAN mix and match your airbrush gun and compressor, but depending on the brand you may have to get an adapter for connecting the two together. It is probably easier just to get a matching set
Finally, in terms of side vs. top feed.....I'd say thats all about preference! Both will perform the same.....the advantage of a side feed might be that you can attach a bottle feed to it if you need to do body painting or anything large scale. Otherwise I'd say the top feed is going to be more effecient with foundation products.
Hope this helps!