Kudos for going for it. You have probably tested the deflection (relief) by fretting the low E at first and last frets. In the middle you should have about a .01" gap between top of fret and string. (You can use an old guitar sting around .010 as a feeler gauge.) That measurement is not absolute. I usually set it as flat as I can get it without buzz. Around .006 in my set up. If you get too flat, you'll start getting some buzz.

If you have no buzz, you are probably have enough relief, but you can check and make sure you don't have too much, too. Too much will make it harder to play and throw off intonation.

If you put on new strings and were used to dead ones, you'll hear the strings ring amazingly long and clear compared to an old cruddy set. This may be all you are concerned about, and it's actually a good thing. Unfortunately, it does not last. :p

p.s. With any new guitar, I always look to the nut first. If it needs reslotting, you may want to take that to a pro. There is a set of guiding measurements for each slot, but you can easily check by fretting each string at the first fret and make sure it does not go sharp. Use normal pressure. The low E for example should hit exactly F. Chords played close to the nut (ie open chords) are highly affected.

Hope that helps.