http://www.samys.com/index/page/product/product_id/5105/product_name/EF+100mm+f2.0+USM+Autofocus+Lens+(58mm)

It depends what your taking photos of. Lets assume you are taking photos of a 6 foot person, full length. At 100 feet, the angle is about 6 degrees. With a crop sensor, this requires a 200mm lens at the long end. At 50 feet for a 6 foot subject the angle is 12 degrees. 100mm would be close to the right size to cover this.

A 4 foot subject would need ~320mm on the long end, but you don’t have money for that.

Now, if your going to be on a tripod all the time, and you want to bump up against the $600 price point, the 70–200 f/4L is the best your money can buy. Even takes 58mm filters. But, it doesn’t have IS, so camera shake will be a problem if you aren’t on the tripod.

IS lenses are strongly recommended if you will be doing any work away from a quality tripod.
The 18–200 f/3.5–5.6 IS is a do-most-of-it-all lens, great for walking around and may replace all but your low light stuff. But it takes 72mm filters and is close to your price limit
The 55–250 f/4–5.6 IS at under $300 is your best bet. IS will give you three extra stops, so don’t worry about the speed of the lens so much. You can shoot at ¼5 of a second and still eliminate camera shake, as long as your subject isnt moving too much.

Someone else can chime in on Sigma and Tamron stuff. Just remember you need a lens that covers 100–200 if your frame is 6 foot. IS, Image Stabilization is needed if you are not on a tripod.

This is the lens I am looking at. I want it to be able to shoot closer pictures of mountains, birds, buildings. etc. My current lens just doesn’t have enough zoom to get the pictures I want.

Well, that is an EF lens for full frame bodies. Its ok if you think you will upgrade to a 1D or 5D, but otherwise you will be paying much more than the 55–250. One thing this lens has is the DO glass, which helps with chromatic aberration, which can be a problem if you shot white birds.

Buildings?