Let me get the true, but cliche sounding, part out of the way. The most important thing to show up to class with is an open mind. Now that I've given the yoga answer...
If this is your first class I have a limited number of props and mats that you are welcome to use. If you find that you are interested in doing yoga on a regular basis here is a list of things you may want to have for a class or home practice.
You need your own mat. The main reason is that this is the most sanitary option. People sweat all over yoga mats. I do clean them after each use, but being a bit of a germaphobe myself, I feel like this is really important. Mats can range from as low as $5 to the $100 and above range. If you get a cheaper mat, just use a towel to help keep you from slipping.
At least one yoga block. Two blocks are ideal. They can be used in supported back bends, to help you sit up straight in seated postures, etc. Yoga blocks come in all kinds of sizes, colors, and materials. I like the firm large foam ones. They are a REALLY useful tool. I usually buy them on ebay.
Straps are also very helpful, but not necessary. Straps are helpful in postures such as forward fold if you aren't yet able to reach your toes. I have used belts, scarves, towels, etc. Like everything else associated with modern day yoga, they can be super affordable or really expensive.
A bolster. These generally are necessary, but they sure are nice. The issue is that I haven't see one that doesn't require a pretty steep monetary investment for something that is simply a glorified pillow. I have an extra large one that is fabulous to use for supported savasana and many other postures.
Online and in many stores, you can find yoga starter kits.
Start with the mat and we can work from there. Even if you don't have a mat, bring yourself. In truth, you is all you need. Yoga is about working with that you have.