Does anyone have some suggestions on certifications or classes to take for Information Technology to build up a resume?

No matter what you do in IT, always always always keep up with A+, Security+, Network+ and even Linux+. Getting to things like Certified Ethical Hacker require other security based and code (programming) based certifications. CompTIA's website covers a lot of this stuff.
The main question is, though, what do you want to do in IT? The answer to that question alone can direct you to the certifications you need to pursue.

That type of question is too open-ended, kind of like "which sport should I play if I want to become an athlete?". It really depends on what aspect of IT you are pursuing (telecommunications? hardware? networking? ....), and where your desires lie for sub-skills within those areas.

A great article I recently recently read on tom'sIT PRO should give you a good grasp of the certifications out there and the various IT fields (http://www.tomsitpro.com/articles/best-it-certifications,1-1352.html#best-it-certifications%2C1-1352.html?&_suid= [login to see] [login to see] 134531556)

When you do start down the path of pursuing your certifications, make sure you take advantage of SkillSoft (https://usarmy.skillport.com/skillportfe/custom/login/usarmy/login.action). The Army has purchased enterprise agreements, so all the training on these sites are free to the Soldier.

Additionally, the Army has vouchers to pay for IT certification exams - but they are getting harded and harder to come by. Details at https://atc.us.army.mil/iastar/news.php?module=attachment&id=38

SPC Bogenschutz, there are a ton of certifications you can get. From the basic A+ Cert all the way up the chain. I'm currently getting set to start a course to get my PMP (Project Management Professional) Certification. But honestly, I've been doing IT stuff since I was in the Army and to this day, I carry zero certifications. There are a lot of things the military teaches you in relation to IT. Feel free to send me a direct message and we can discuss further based on your skill set or we can keep sharing ideas here which hopefully someone else getting ready to transition will see and find useful.

Comp TIA Suite is great:

A+
Network+
Security+ (Depending on what you will be doing)
CCNA
Windows 7 is a great one to get because its an enterprise system
CISSP or CASP after Security+

You can also look at the following if you want to get into management:
Six Sigma (which operates a good deal like military projects)
PMP: Project Management

Plenty of military support to help get these as well.

SSGT GREGORY G. Only get a Cisco cert if you want to make a lot of money & always have a job

A+ is a really simple cert to study for and learn if you've done any work in the field with desktop computers/servers/hardware. Net+ gets more into the network side but still builds some off of A+. Security plus is a more detailed version of them both combined and much harder than either one. Study, study, study. Memorize your ports, learn IP addressing and so forth. Next step would be CCNA (step in another direction but a step forward also). You can land some pretty good jobs making around $70k a year with those in your back pocket even without much experience. You need to get a degree in IT or computer science also. Going to college and getting a degree shows your employer that you can stick to something and complete it. It's not just about the knowledge you gain but also the hard work you have to put into it.

Many of the contracts I have been selected for was because I have the CompTIA A+ Certification. Several more now require the Network+ and Security+, and I have missed out on several opportunities because I didn't have Microsoft Certifications. If you really want to confuse people, you could become a professional hacker with the Certified Ethical Hacker credential. It's gaining popularity in the security field. It's funny to me to tell people I want to be a Professional Hacker and see the expressions on their faces!

Anything by Cisco

I went to my local junior college, a fine school, and asked the same question a few years ago. Under the guidance of the Dean of Engineering, I earned certification in CompTIA A+, Network+ and Security+, as well as an AS in Computer Science and an AAS in Computer Systems/Information Systems.

The CompTIA certifications won't get you a job; they will just prevent you from being disqualified for a job, those that care about it. Also, IT employers tell their employees to study for their A+ cert when they aren't busy; it's something easy for employers to tell employees to do to keep them busy. It's funny, because I've gotten my last few jobs with or without it, even though they all "required" it, and even though I've regularly informed my current employer that I'm certified, my manager still asks me every few months if I am. So, pass the tests, just to get them out of your way.

Depending on what job you are trying to get, your employer may not care very much what certifications you have. CompTIA A+ is just the bare minimum certification showing basic computer competency. Again, employers only care if you don't have it, not if you do.

If you want your certifications to mean something (as in, higher pay or greater employment opportunities), you need to go well beyond the basic certifications that everybody else has. I was going for Microsoft Server 2008 certification (not offered, anymore), but my current employer could not care less if I got it. Actually, now that I have a job, the question is what certification will I have to get this year. It changes every year, depending on what happens to be in demand that year. Last year, we all had to get basic Mac certifications. My employer even paid for the first Apple Mac exam. At the same time, my manager said not to go beyond the basic exam. This year, it looks like Microsoft Office Anywhere/360 is going to be in demand.

My recommendation is to look at the kinds of jobs you want, analyze the requirements, and then do a Google search to determine what certifications and education are required to support those skills.