It sounds like you definitely want to stick with a spinning rod combo. Since you are wanting to keep it under $100 and are just getting back into fishing. I grew up using a spinning rod combo in the Uinta lakes. I would try and find a nice 2 or 3 piece spinning rod from a reputable company. My favorite spin rod for backpacking is a Berkley Trout Series Ultralight rod that I picked up about 15 yrs ago. It's a 6' rod that breaks down into 2 pieces. I picked it up on clearance for under $10. I don't think they make that exact rod anymore but you should be able to find something similar for $30 or less. For a reel you are going to want an ultralight reel to match the rod. I prefer closed face spincast reels because I have had way less problems with them than open face reels. I also prefer the "underspin" style of reel. Like this
http://www.basspro.com/Daiwa-Unders...15_11128_530bad75e4b021b76fd3b5df_41408680111
You should be able to find a nice one for around $20. All of the lures that others have mentioned previously on here are good lures. I would add to those the Panther Martin series of lures. In the Uintas you are going to want to stick with the smaller sizes. I would definitely also go with a bobber and fly trailer setup. You can get flies at Sportsmans Warehouse for $1 each or there are some places online you can get them for $0.50. I get a lot of my trout flies from
www.streamflies.com. All their trout flies are $0.50. If you are going to buy quite a few of them then the shipping isn't bad. In Utah you can actually fish with three flies on your line. Three can get a little messy but I would definitely recommend fishing with two. You want about 6' between your first fly and the bubble. I like to use a surface fly for the first fly. Get something that has foam in it like a foam beetle, ant, grasshopper, etc. It will float a lot better and longer if it is foam. Then tie on about 18" of line to the bend of the hook of that first fly and put a nymph fly on the bottom fly. Some good all around nymph flies are, Hares Ear, Pheasant Tail, Prince, Wooly Bugger, or any style of midge larvae. I would stay away from the bead head nymphs as they will tend to pull the first fly under the water to much. I will often get into two fish at the same time with this setup.
A few people mentioned casting distance above. I have found this not to be an issue in most lakes. In lakes, fish come into the shallows to feed because that is where the aquatic life is at. The only trout that feed in deep water are lake trout(non in the Uintas that I know of. There are a few lakes in the Winds that have them). You are more likely to find fish feeding in the more shallow areas of a lake than you are the deep areas. In the summer months the fish do go to the deeper parts of the lake during the day where the water is cooler but that is when they are not feeding. When they are feeding, they go to where the food is, in the shallower areas. Shelves in lakes are also great places to fish. The fish like them because they can feed in the shallow water and then dart into the depths if a predator comes along.
Others have mentioned fly fishing. I love fly fishing and that is what I do 99% of the time now but there is a bit of a learning curve especially fishing lakes and the equipment can be quite a bit more expensive. I do find it much more involved and pleasurable though. In your position I would stick with spinning gear for now. Tenkara, like others have mentioned, is a great ultralight backcountry setup but it is definitely more suited to streams than lakes.