Best sports bike for around 4,000?

I'm currently riding an 85' honda shadow 700cc. I'm six foot 250 lb 18 years old and want to buy my first sport bike. I want to spend around $4,000 for my next bike. I want something faster and bigger.

Tl 1000 r

Take your time looking and don't jump on something, be open to several bikes, and find something in great shape… Have the money and be ready to buy because a good deal won't last, but you will find something for that amount in really good condition, don't settle for less.

Any sport bike will be alot faster then a shadow, get a cbr 600 or gsxr 600. Both of those bikes have about 3x the horsepower your used to.

I'm 6'2" and 220 pounds. I would recommend a GXSR 600 or the ZX6R. Like Blair said, any 600 will have roughly 3 to 6x the power ratio than the cruiser.
Your best bet for sport bikes, is sizing each bike to yourself. A few tips to sizing one, as you don't want to buy it and hate it a month later because it's uncomfortable to ride.

Head to your local bike store and sit on all of the bikes. When you sit on em, keep a couple things in mind. Your legs WILL be cramped. They will get used to that with riding.
When you sit on the bike, put your hands on the bars, but don't put any weight on the bars. Use your legs when you ride a sport bike. When you sit on the bike, your legs supporting most of your bodyweight, and your abs to support your upper torso.
You shouldn't be too stretched out or too compact on the bike, or your back will hurt like hell.

Usually for guys in the 6 foot and up range GSXR and Kawi are a little more comfortable.

Hope this helps.

If you are a starter, start with a 600. Id say used R6, or if you want something weaker go with a bandit 600.