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.