Seasick- I'd decide exactly on what dimension/size tank you want first. A 20g long or 20g high? 30's aren't a typical off the shelf tank, but 29's are. They're basically a tall 20 long.
I beg to differ Freshy. 30 gal tanks are most certainly an "off the shelf" tank. 36"x12" is a great footprint for a starter tank.
To the OP, the recommendations you are getting about upping your school of neons are certainly valid. Small fish like that look much better in bigger schools. 5-7 fish in a 30g would certainly be "lost". They get separated, they don't see each other and then they end up hiding. Larger schools are much more visible so if an individual fish gets separated, there's a much greater chance it will see it's mates and rejoin the school.
I had a 30g at one point that was heavily planted, it had 25 cardinals, a few cories and a few otto's and a pair of kribs - with no issues whatsoever. While I'm not recommending that you do this from the start as you are a newbie, with proper knowledge and understanding that will come in time, you can progress to that point.
A heavily planted tank can always hold a bigger bioload that a non planted tank. Planted tanks are great, but again, they require a lot of knowledge and understanding that you can certainly get from visiting forums like this one (among others)
Best of luck in your endeavors,
Roy