1600MHz DIMMS are listed on the support list, however not your specific DIMMs. With that said, it should work, they can't list every single module that every single manufacturer makes, so as 1600MHz DIMMs are listed at higher specs than yours (CAS 8 rather than CAS 9), I would say it should deffinately work.
For the initial build, I would change the case and that is all. The Antec 300 is an ok case, but like nearly all other Antecs, cable management is awful, and especially an issue with the 300 is the price, you can get much better cases for your money. Assuming you are in US and paying Newegg price which is ~$60, $10 extra will get you a CM 690 II which is arguably the best bang for buck case on the market:
or, for less:
which if you don't like the styleings, you can get the same case with different, "plainer" looks for $10 extra:
Newegg.com - NZXT BETA EVO Classic Series CS-NT-BETA-EVO Black Steel / Plastic ATX Mid Tower Computer Case
With the extra money, getting another case fan would be a good option as they only come with one