Yes that would work great. Many have had it done and are very happy with the results. Keep in mind gears/tlok don't add hp, but better distribute power throughout the powerband giving you much improved acceleration, launches, and 2 wheel burnouts
Gears are about $150 and and tloks are ~$200. Tuners are $379 and installs range from $300 to 500+ depending on the shop. I'd recommend getting them professionally installed. Gear installs require a lot of attention to detail, a good amount of precision, and patience. Experience is key since any slight mishaps can cause grinding, rubbing or larger problems in the future.
Typically manuals favor 3.73's and autos stick with taller 4.10's. You can run 4.10's but keep in mind that 1st may become "useless" and mpgs will decrease slightly, ~.5-1mpg on the highway. Your gas mileage will probably rise slightly in the city. I'd say the slight loss in highway mpgs is worth the performance gain.
Another option is to look for an 8.8" rearend from a 94-98 GT or Cobra. The 8.8" is much stronger and comes with a limited slip differential (tlok). Depending on the condition and mileage of the rearend, you may want to install new gears and rebuild your tlok. American Muscle sells rebuild kits with new carbon clutch discs, shims, and s-spring.
Check craiglist, ebay, and local salvage yards for wrecked v8 cars if the larger 8.8" interests you.