Jaiden,
As Frank II mentioned, the first step is to pick up a copy of Europe Through The Back Door, as that will provide the information you need to plan your trip. It also covers things like "rail skills" (very important!), money and language issues.
You might also want to have a look at some of Rick's shows on PBS (OPB or KCTS Seattle in your area?) as that might give you some ideas on places to visit.
You didn't say how long this trip would be, what type of budget you're working with or what time of year you'd be going? Travelling with a group is certainly one option, but would undoubtedly be more expensive than going on your own. However, tours are a good way to get an introduction to travelling in Europe, and can provide the skills and confidence to go solo on the next trip. My travel method for the last few years has been to take an ETBD tour and then travel for an equal length of time on my own (the best of both worlds!).
If you want to have a look at Rick's tours, click the "Tours" tab at the top of this page. You'll probably find that you meet people along the way (especially if you're staying in Hostels) and you could also take the occasional day tour in various locations, which would give you some time with a group.
The topic of young women travelling alone has been raised here on the HelpLine several times before, and the recommendations have been somewhat "mixed". From a parent's perspective, I'd probably be a bit concerned, but with adequate preparation you should be fine. I'd suggest travelling with a Cell Phone though (use text as much as possible as it's cheaper).
When I'm not with a tour, I travel solo and find that I like the freedom to explore places that interest me, without any time constraints. The aspect of "loneliness" is certainly one aspect of solo travel, but I find I'm usually so busy touring and visiting that I don't have much time to dwell on it.
Good luck with your planning!