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If you aren't able to do the restoration yourself and you don't have a friend or family member that can help you out, find a shop that you can trust and that will work with you. You'll find many shops either want to force you to spend more cash than necessary, or want to do things completely their way. Look around for recommendations.
As far as the fun factor goes, a V8 is the only way to go unless you want to do something radical like a twin turbo straight six. 289s and 302s are a dime a dozen in many places (except out west, apparently), and you can build them up pretty reasonably without blowing a ton of cash. I'm estimating I'll spend $2-3k total on mine, and I will hopefully be in the ballpark of 350 HP. Engines in this family include the 289 (the original V8 for '64-68 Mustangs, IIRC, alongside the 302 and 351 from '67-69 and forward), 302, 331 stroker, and 347 stroker. Essentially, they're all the same engine with a different crank and therefore different stroke length. 351 Windsor (351w) blocks will also fit, though it may be tight without some exhaust modification. There are 351w stroker kits in the range of 408-427ish, but you'll need to significantly strengthen the car for it to withstand the torque. 351 Cleveland engines (351c) might fit with extensive exhaust modification, but most agree it's not worth the effort - there are more aftermarket parts for the Windsor anyway. Finally, big blocks (390, 427, 428, 429, 460, etc.) will NOT fit in a '66 without spreading the shock towers (a very extensive and radical mod). If you want to run a big block, pick up a '67 or later.
As far as transmissions go, you can look around for an original 4-speed toploader (I bought three, since they were getting hard to find) in decent shape, or retrofit a Tremec T5, TKO series, or AOD if you're into automatics. The 4-speed toploaders were absolutely bullet proof, and will bolt right up as long as you have the correct bellhousing, linkage, etc. T5s, TKOs, and similar transmissions will require some modifications to the car (I'm not exactly sure what, I haven't considered one myself), but will eventually bolt in. T5s are a dime a dozen, but they're much weaker than the toploader or the TKO. Generally speaking, if you want it to be era-correct, get a toploader. If you want a fifth (overdrive) gear to keep the highway RPMs down, get a T5 (inexpensive but weak), or a TKO (expensive but strong). You're lucky to already have a manual car - the clutch and brake pedal assemblies are extremely hard to come by (unless you find a donor car). I paid $135 for mine, since no one that I know of makes an aftermarket solution.
Finally, doing a V8 swap isn't as simple as taking out the old and dropping in the new. You'll need to swap in V8 spindles and convert over to 5 lugs, and you'll want to trash the stock 7.5" differential and grab an 8" from a '65-66, or a 9" if you can find one. The 8" is plenty for general street cruising and below, say, 300-350 HP. If you're running slicks, considering a turbo or blower in the future, or dropping the clutch at every light, you're going to want to upgrade to a 9". The 9" rear ends are fabled for their strength, and are used in hundreds of projects - drag racing, offroad trucks and jeeps, Fords (obviously), Chevys, Mopar, etc. They're also very hard to find for a '66, since our cars are narrower than the '67 and on. The '65-66 9" rears also had tapered axle tubes due to the smaller shock plates and U bolts. IIRC, they only came as an option on GTs, or standard in Shelbys. On the other hand, you can also get a wider 9" from a '67 and on and modify it to fit, or even do some heavy modification to a newer 8.8".
I'm sure unless you're a car nut or have already done some extensive research your head is starting to spin. There's a lot to learn (I'm 2 years into the project; started with a rust bucket that needed a LOT of attention), but it can be extremely enjoyable. Don't expect to have the fastest, safest car in the world and certainly don't expect to ever get whatever money you invest in it back. Do expect to turn a lot of heads and get a lot of comments, though. They're only about 2600 lbs stock, so with a semi-build 289 or 302 (heads, cam, intake, lighter pistons, stronger rods), a decent transmission, a stronger differential, and a better final gear ration (~3.55-3.73 for a 4 speed, 3.73-4.11 for a 5 speed), you can have a lot of fun for not a lot of cash.
Edit: I forgot to mention that upgrading the suspension is a good idea. You don't need to go all out and get IRS, tubular control arms, etc. Some stiffer springs, better shocks, newer leaf springs, a Monte Carlo bar, export brace, and subframe connectors will go a long way to stiffening the car up and making the ride much more enjoyable. Everyone I've talked to said subframe connectors were the absolute best thing they ever did with their car.
Mustangs Unlimited is a great place to buy parts (I'm lucky enough to have one ~30 minutes away, but you can order online as well), and it's hard to beat Summit Racing for aftermarket engine parts. For bigger things like transmissions, junk yards and swap meets are your best bet, unless you want to throw down two grand on something "new." Finally, MustangForums.com has a wealth of information in the classic car section.
