You will probably want to go to www.tsp.gov and read through the FAQs I think to get the best summary, but here's quick answers to your questions.

I've been in the Guard/Army Reserve for many years, but have never enrolled in the TSP. Is this something I can enroll in while continuing to max out on my IRA contributions?

Probably. The closest comparison is that it's like a 401K plan, but generally with no matching contributions. The fund options are extremely low fee compared to many other 401K plans, and most of us are happy with the funds' returns. They even have lifecycle funds now.
http://tsp.gov/features/index.html

If you make too much money :) you might not be able to deduct your entire IRA contribution, but for most of us that's not an issue.

The one caveat is that if you are deployed, and you make tax free money by working in a combat zone, you probably want to sink as much of that income as possible into a Roth IRA so its earnings will stay tax free, because if you put tax free combat pay into your TSP, its earnings will be taxed on withdrawal. The initial tax free contribution will be tax free later, but that hit on earnings would stink.

Also, what are the special benefits of the TSP? Is it like a Roth or conventional IRA? Does the government match your contributions in any way? Are there any tax benefits?

The government has authorized the services to make matching contributions, but so far I think only a couple of super hazardous MOSs qualify for the match. The tax benefits are similar to the 401Ks.

http://tsp.gov/features/chapter03.html

You can also later roll your contributions over to an IRA, just like you can with the 401k plans. You can also purchase a lifetime annuity.

-Heather