There is obviously a wide range of options, with a commensurate wide range of prices.
At the low end would be a SBF donor engine from a 1995 or earlier Mustang GT. You can pick these up used or from salvage yards and you'll have a very affordable engine and transmission - though condition could be an issue. Obviously these will be fuel injected, so if you want to go carburetor there are a number of changes to be made - as documented here:
EFI to Carb conversion..... - Ford Mustang Forums
OTOH, you may want to leave the FI in place for cost reasons as well as the need to pass inspection, including emissions testing. I'm not in CA, so I'll let others weigh in on that issue(s). If you go with an injected engine you can always switch to carburetion later. This would also have the benefit of allowing you to get used to driving a light weight, short wheelbase car before you start playing with more power - though it won't have the lumpy idle and throaty sound some people associate with Cobras.
Stepping up to the next level you'll find mass-produced crate engines in varying displacements, from long blocks all the way to fully dressed. These are widely available from suppliers such as Summit Racing and Jeg's. I have no experience with these, I just see them in the catalogue. Here's an article from 2006 that talks about various crate engine options:
http://www.mustangandfords.com/parts...-engine-guide/
Custom engines are available from a number of builders, as previously noted in the thread. These are going to be more expensive, as you've noted, but you do get what you pay for. The builder will work with you in terms of what you're looking for, what it's going in to, your intended use (e.g. street, drag racing, autocross, road course) best setup for your transmission and final drive ratio, etc.
As the old saying goes, "speed costs money, how fast do you want to go?"