The line #7 on the rod refers to the AFTMA standardized line wt designation. It means that you should buy a 7 wt (or #7) line for proper loading and best casting efficiency with the rod. I would recommend you get a WF7F (weight forward 7 wt floating line) for the rod.
Regarding your question on whether the line # has anything to do with what reel to use on the rod, the answer is a qualified yes. You need to get a reel that will hold the WF7F line and about 100 yds of 20lb dacron backing. There are many very serviceable reels available for the $120.00 or less that you set as a spending limit. You don't need to buy the expensive macined disc drag reels that many experienced fly fishers use, all you need is a reel that will hold the line and dacron backing. Okuma, Pfleuger, Martin, STH, Cortland, and Scientific Anglers (known as SA) are only some of the reel makers with reels in your price range that will work.
The best way to get a reel, line, and backing for your T&T rod (by the way, T&T is one of the premium and best rods makes on the market) is to go to a fly shop in your area. If I'm not mistaken, there is at least one in Roanoke. The guys in the fly shop will be able to help you select a reel that is less than $120.00, a WF7F line, and will even load the backing and line on the reel for you. Additionally, the folks at the shop would probably provide you with a quick lesson on how to fly cast and could put you in touch with other fly fishers in your area who could help you in your learning how to fly fish.