If you look back in this forum (new riders), you'll see lots of threads on "first bike", 250", "600" etc. which discuss the relative merits of different classes of bikes as "first bike". You will find lots of recommendations against an R6 or CBR600 as way too much power for a first bike. Kawasaki has made the Ninja 250 and 500 for many years which are both viewed as great starter bikes depending on your level of experience. They are sport bikes (good looking as defined by most), reasonably priced, and readily available used well within the price range you mentioned.
A twin 500 or 600 (Suzuki GS500 for example) is also a good way to go. You will also find lots of advice to stay away from a bike with a fairing as the plastic parts are expensive and readily broken when the bike is dropped.
At your age, insurance is going to be a major expense especially if you need full coverage (liability plus theft and collision) required if you have a loan. If you can swing paying cash, that would be better at your age. Just remember that without full coverage, if the bike is damaged, totalled, or stolen, you're SOL.
In your list of riding gear, don't forget pants, gloves, and boots in addition to the jakcet and helmet. What part of your body can you do without? If you don't have any street riding experience, you will also find lots of suggestions to take the MSF course first. That will be another good way to find out if street riding is really what you want. HTH and good luck.