Ford has a crate, pushrod, Boss family engine with 363 cubic inch displacement, 500 HP, 450 lb/ft torque. $8595 Too much for the budget? 306 cubic inch, 340 HP, 310 lb/ft torque. $3845 A few options in between.
Spend your budget how you want, but at $6999 for the coyote, plus fab and trouble shooting, a crate Boss engine might give you better bang for your buck. It's hard to argue at less than $4000 built.
An Optima battery would be a good choice. You need a battery with at least 500 cca, check out your local parts store and have the battery box measurements. I'd think a group 34 would probably fit and should offer enough power.
I'm building a 351 to drop in the Cougar, the block is at the machine shop. It's getting an .030 overbore, stock crank, new pistons, rods, etc. I'll be running carbed. I'm curious as to your opinion on heads. Budget at this point rules out new aftermarket, but how are the e7 302 heads? I can get a pair reman at about $360. GT-40 heads seem hard to find. Any other good casting #'s to hunt for???