I may be one of the few people on this board to have both carb and EFI with the same engine in the same car. I started with a new Ford Racing GT-40 crate motor and put an Air-gap intake and both a Holley Street Avenger carb and then an Edelbrock Thunder AVS carb, each time dynotuned. It ran fine (better with the Edelbrock), had plenty of power, fired up right away and sucked gas and spit fumes like you'd expect.
Just after finishing it up, getting it all dialed in and tooling around for a bit, I decided that I didn't want the project to end and was intrigued with EFI. Having had two different 5.0L Mustangs, I liked how they ran, so off I went ...
Bottom line is that the carb was plenty reliable, relatively simple and worked pretty well except for the mileage (or lack thereof). That said, the EFI is better in EVERY way with the exception of cost, looks (though I think it looks just fine in a non-stock Mustang) and extra installation effort.
The swap can be as easy or difficult as your build and budget dictates. To keep costs down, stick to as near a stock 5.0L setup as you can so that you can use take-off parts. Once you start getting into a performance build, you're looking at costly performance throttle body, intake manifold, MAF meter, fuel injectors, etc. Also, costs can be reduced if you modify a stock 5.0L wiring harness.
If you want a simple install (and are willing to pay for it), get a fordfuelinjection.com harness and Ron Morris performance fuel kit (includes everything you need). FWIW, I do not have a baffle or surge tank and have NEVER had so much as a hiccup with my EFI, even on hills. Granted, I have a 20 gallon tank and I don't think I've had it much below 1/4 full. If it is a concern, buy a '70 tank which holds 22 gallons and pretend like you still have the 16 gallon stock tank, problem solved. :-)
Can't help you with all the auto stuff as mine is a T-5. Finally, no matter which way you go, I recommend reading through fordfuelinjection.com to see how these things work, and then James' site to see how to apply this to a classic Mustang. I've looked at plenty of sites and his is the best that I've seen. Even if you don't do it exactly like he did, it'll point you in the right direction.
Oh yeah, my battery is still in the stock location!