There is no question you want a road bike, and you can save a pile of money buying used. However, as a newbie you need a proper fit. One solution may be to see if there is a shop in your town that sells used bikes. Another option is often shops have bikes that are one, or even several seasons old that they will heavily discount. A last option is cycling clubs with classified sections. While you can't be fit, you can at least test ride a prospective bike since it will be in your local area (same goes for craigs list) wherease ebay bikes, while a good value, are unlikely to be test rideable.

On wheel size, its not the wheel size, its the combination of wheel size and gear that makes you go fast, so while you need to be in a different gear on a smaller vs larger wheel, there is negligible difference in power transfer. However, tire weight and tire width do have a big imapct on speed, lighter and skinnier (for the most part) is better, which is why a road bike will be better than a mountain or hybrid bike.