PrPor can certainly do most of what you want/need. Some of this will depend on your Assets. I hope that when you did the telecine work, you got either DV-AVI Type II files, or AVI uncompressed. These will allow you the most correction with the least loss in quality. While there is some compression with DV-AVI, you'll likely never be able to find this. One big note: if you go with the trial version, it will not touch anything MPEG.
As for the correction techniques, you are not really limited. PrPro has almost every tool that you could ask for. I've use it to restore many very old, poorly stored VHS tapes, and some were even shot in LP and EP. For more extensive work, AfterEffects would be the go-to program. Still, I do not think you would need to go that far. If one of the suites, that includes AE fits your budget, that might be a good choice.
You might want to try the trial version of CS4. It's got a 30 day period, so you might want to have things ready to go. Create a Project to match the frame size of your Assets, and Import a few. The learning curve seems worse, than it is. Actually, I find PrPro easier to learn and use, than PE. Once you have your Project set up, people here can step you through most questions that you have. As what you do will be dependent on your Assets and their condition, it's not really something that one can give you a formula as to how you should correct.
I'd begin by looking at the Levels Effect (and maybe Highlight & Shadow), then one of the Color Correctors. These were common to my VHS restorations. Since you will be getting a fair preview on the Monitor Panel (for highly critical work one needs a calibrated broadcast monitor, but for something other than commercial TV broadcast the preview is good), so much will be by looking at your Effects and their result. It takes some time, but once you get into it a bit, the folk here will be glad to make suggestions.
Learn how to do screen-caps of your computer's monitor, and attach these to your posts. Seeing approximately what you're seeing will help them. If you already have this down, just be prepared to use that technique fairly often, until you develop a scheme.
Within 30 days, you should know for sure if PrPro can do it for you. I think that it can do all you want, and more. If you are restoring these for a large-screen theatrical presentation, then you will want to add AE, without a doubt. For almost anything less, you should be good to go.
If you do decide that this is the program for you, do read the entire Help file - if there is still a manual (lost art now), read it daily. These will help you pick up on the terms used in PrPro and help others to help you get the most out of your program and produce the best from your Project.
Another great resource is the PrPro-wiki. There are great tutorials and the FAQ section is not to be missed.
Others might have more input, so be a bit patient,
To put it simply, Premiere Pro is for professional editors, people who have been schooled or trained in video production. Premiere Elements is for the average person who does not have a proper education in video production, but still wants to edit their videos.
Both will do what you want, I believe. The more salient question is which category of user do you fall into?