OK, so some legit advice would be to talk with your security folks long before you tie any knots. The worse thing you can do is get married in a drive-thru in Vegas by "Elvis" and then show back up base hand-in-hand expecting everything to be hunky-dorry. If you have an SCI clearance, your SSO will know what to do as you won't be the first person to marry a foreigner.
If you get married before OTS it shouldn't be a problem, you won't need anything more than a secret (collateral) clearance to get you through UPT. If you require higher clearances, it may take a bit longer with your Czech wife, but like many have said, it is easily done as long as you are up front about everything. In other words, don't lie as they will find out and that will put you in deep shit.
And congrats in advance if you do marry this girl; I spent a little over six months in the Slovak Republic on a military liaison team and I did see a lot of beautiful women there! However, I was already engaged and my future bride had my motorcycle hostage, so I had to behave!
Cheers! M2