I've been hunting all sorts of game (deer, hogs, etc.) with crossbows since they became legal in Texas. I am a disabled veteran, and like you, I had to switch to shooting a crossbow during archery season because I couldn't hold back my Mathews compound bow anymore (due to arthritis). Although there are several crossbows out on the market today under $500, you have to ask yourself a couple of questions first:
1. Comfort: How balanced does the crossbow feel to me when I hold it? Am I able to set the crossbow with the rope pulley provided, or do I need a hand crank winch to set it?
2. Parts: How easily can I get replacement parts (ex: strings) if needed? Can I get the recommended bolts?
3. Repair: Will a local bow shop be able to provide repairs/service on the crossbow if something happens?
4. Accuracy: I highly recommend you do not buy any crossbow unless you get a chance to test shoot it a couple of times. Some models look good in the shop, but don't feel so good when you actually shoot them.
I own two crossbows; my first was a Parker Tornado. It shot great for a couple of years, but now the limbs are starting to splinter. When I contacted Parker about it, they told me the only way they could repair the bow was for me to send it back to them. I really didn't want to go through that kind of shipping hassle (plus they completely changed the nocking system on their crossbows after I bought my model), so I started looking for another one. I finally ended up buying an MXB-360, a product of Mission by Mathews. I've been trying it out this summer prior to archery season, and it's an awesome crossbow. It's very comfortable, I can easily get parts/service for it at my local bow shop, and it is deadly accurate.
Unfortunately, both of these models are over $500, and it sounds like you are trying to stay on budget with this purchase. That being said, I have read good reviews about the Excalibur series. Some of their models (like the Axiom), cost just a little over $500, but sometimes it's better to spend a little extra money to get exactly what you want and will want to shoot for the next several years, versus buy something simply because it's cheaper, and it ends up being nothing but misery trying to shoot it. Just like with a compound bow, you want to do your research, test shoot a couple different models, and then decide what is most comfortable shooting for you that is within your budget. I wish you the best of luck with your future crossbow purchase...you won't regret it!