Jody - welcome to being a HAM radio operator.
First the easy answer - you just need an analog radio. Digital doesn’t have a large install base and is also rather expensive. A simple 2 meter single band mobile is very inexpensive and will likely be your first choice.
You could opt to go with a handheld but they are usually 5 watts with a couple of them at 7 watts and that might be enough when combined with a mag mount antenna to hit repeaters 10 to 15 miles away but that isn’t going to work reliably for simplex work when chasing or when you are further away from a repeater.
My favorite 2 meter radio is the ICOM 2200H -
http://www.icomamerica.com/products/amateur/2200h/ It has plenty of power at 65 watts. The controls are pretty basic so you shouldn’t be overwhelmed with it. You don’t want something with too many options which can result in some setting/menu you cannot get out of and end up with an unusable radio when you really need it.
(I did program (screw up) something on another one of my radios and after several days of trying to correct it, I just did a factory reset and programmed it again. Not something you want to do when chasing.)
ICOM also makes other good ones plus Yaesu and Kenwood have great choices too. I think you cannot go too far wrong with any brands listed if you don’t buy too much radio and buy new. New comes with manuals and support where a cheap old radio from another ham may not.
Now I did mention a single band radio. Most nets for storm spotting and most chasers use 2 meters. You could get a dual band radio which usually has 70cm but you won’t find that as useful and it will cost more. However, some dual band radios are also dual receive. This will allow you to monitor 2 frequencies at once.
I use this type of radio in my truck. I can monitor the Skywarn repeater net for my local county plus the Skywarn statewide net ran by the Indianapolis NWS office or rag chew with other spotters on simplex while not tying up the repeater.
As for an antenna, magnet (MAG) mounts are good and don’t cause you to drill holes in your car/truck. For some, holes are no big deal and for others, they are. If you don’t mind holes, you can mount one dead center of the roof to get the best performance. However, there are other options too such as trunk/lip mount if you are not in a truck and even through the glass which can be OK.
Any antenna can work but look for one with 3 DB of gain or more for better performance. Just don’t forget if you get a dual band radio to get a dual band antenna.
For a deal on a radio, see if there is a nearby hamfest you can visit that has new dealers. I picked up several radios cheaper than any online store.
Online, I like to shop here -
http://www.universal-radio.com/catalog/index2.html
As for a generally accepted storm chaser frequency, it is 146.550MHz.
Here is my install...