What to do for the best on the exterior of our house?
On a budget, Vinyl siding is the most cheapest, cost-effective option.



Pros


Fairly easy to install
Durable
Comes in a ton of colors/styles 
Low-maintenance (wash yearly, that's about it)


Cons


Can be broken by strong impact, and if cracked, there's not really a patch, you just have to replace the entire section
Very strong winds can rip siding off (though this is highly subject to the wind angle, style of siding, installation method, strength of fasteners, etc)




To install over top of brick you'll have to install furing strips first. Basically vertical strips that give you a nailing surface, installed every 16"  (though siding manufacturer may have specific instructions). 



1x3's would be fine, but you can use a different thickness if you're trying to match up with window trim. There's many ways to install but I'd tend to use masonry screws (eg Tapcon).