A budget of $800 is going to be hard to work with.
I would recommend the PPI BK1800.1 to save money. You're not going to be able to tell the difference between 1800 and 2200 watts after impedance rise and other factors come into play.
What size is your stock alt? If it's small, I recommend getting a high output alt from Mechman, once again because they are usually the cheapest without going with low quality. No matter what you do, you need to replace the battery under your hood with an AGM battery. Duracell AGMs from Sam's are pretty affordable.
And please make sure the guy knows what he's doing when he designs and builds the box or all your money on equipment was wasted...