I've just started storm chasing as well, I will be graduation in 3 days.. Then I will be majoring in meteorology as well at Iowa State.
I would suggest finding a partner, that way you will be much more likely to stay out of trouble. And it is the easiest way to learn something! A lot of guys are willing to take people along, given that you will have to chip in for gas, other expenses... But usually it isn't to hefty of a price depending on how far you go.
The two points I parsed above are what I did. My first time storm chasing was on 8-9-99 in southern MN. From 1999-2001, I chased either by myself or with a good friend who didn't have any chasing experience either. As long as you read all that you can find about storm chasing, storm dynamics, etc, you'll be just fine. Read read rread read read! There is an almost myriad of information on the 'net regarding storm chasing and storm dynamics! If you are looking at making meteorology your profession, start reading all the SPC publications you can! There are other great resources that are a little more basic as well, including U of Illinois WW2010, CoD class pages, and OU Mesoscale Meteorology page. I went through most of the content on those pages before I went out the first time. You don't need to be an expert, but the most you know about how storms behave, the safer you may be.
As I said above, I've never had a problem with going out solo. And actually, I like solo chasing every now and then -- it's very therapuetic imo. That said, it's certainly easier to have another person with you, if for no other purpose than to navigate. Eventually you'll find a couple folks with whom you work very well, and you'll probably chase with other folks with whom you wished you hadn't. LOL. I eventually found a small group with whom I work very well with, which makes chasing more enjoyable and those bust days much more tolerable.
The main issues for a new chaser, IMO are not what you'd expect. When you're inexperienced, the biggest problem is busting your target area and not getting to the right storm at all. So at first, the hazards of the supercell environment are negligible because you're hardly ever in them! 'Armchair' forefcasting and chasing are great, cost-free ways to practice forecasting without the expense of a bust. Learning to forecast takes a lot of time and patience but is worth it.
I think the biggest danger to new and veteran chasers alike is the highway and the vehicles we drive, a far greater concern than any hailstone, tornado, wind gust or lightning strike. Our chase vehicles on the inside and the sky on the outside super-saturate our attention with more distractions than we can often handle. Tagging along and/or having a chase partner to take the extra tasks off of you, the driver, will ensure you can keep your eyes on the road and stay safe.
So, I think it's best to 'tag along' at first so you'll have a better chance of actually seeing worthwhile storms, and remember to pay attention to your driving more than anything else.