There are a few different features to look out for:
Levels of pressure sensitivity; how accurately it detects how hard you are pressing. More levels are better.
Angle detection; detects what angle you are holding the pen at, so your software can change the shape of a brush stroke appropriately, or some similar function.
Size; tablets come in different sizes. This comes partly down to personal preference. You may find either a smaller or larger tablet more comfortable or accurate for your purposes.
Battery requirements; some tablets require a battery in the stylus. Others do not. There may be a trade-off between other factors and the convenience of not having to change a battery.
"Feel"; does it feel comfortable to use and responsive? Is the pen attached by some means, or is it free to be carried about?
Hardware buttons; it's usually helpful to have a selection of programmable buttons on the stylus and/or tablet. These can usually be mapped to various functions, depending on the software being used. Different tablets have a different number of buttons, in different positions.
Software compatibility; does the software you want to use the tablet with support tablets? What software does the tablet claim to support?
Illustrator is perhaps a bit more specialised than Photoshop, limiting a little what you can achieve with it alone. However, there are many free and lower-cost packages that offer similar functionality both to Photoshop and Illustrator. For Graphic Design, vector graphics software often makes sense, and can be an important tool. However, raster graphics are also necessary.
Illustrator is for vector graphics, Photoshop is for raster graphics. Other software packages, both commercial and non-commercial, do exist for both tasks.
If you are good at learning new software, you don't have much to lose by choosing a non-Adobe solution, because you will be able to take the knowledge you gained using other software and use it with Adobe software later on. If, however, learning a software package is a major investment of time and mental capacity for you, stick with Adobe so your skills will be relevant to employers.
Beware of the common misconception that says that Graphic Design is all about computer graphics. It isn't, though many of the less reputable colleges would have you believe this with their array of glorified, graphics-specific IT courses. The basic principles of Graphic Design transcend the medium that is used to express them (and different media come and go like the wind). Make sure you learn the underlying theory and brush up on your non-computer drawing, printing, painting and collaging skills, too! Design employers look positively upon such experience, even if the jobs they offer are entirely computer-based.
