Interested in camera lenses

Hi, I would like to start to take better photos. Right now I shoot in manual mode, Nikon RAW, here is some info on what I have now based on that you can help me get new lenses.

I would like a good lens for sports photograph and another for landscape and then a third for people and events.

Current Camera:
Nikon D5000

Current Lenses:
AF-S DX Zoom-Nikkor 18-55mm f/3.5-5.6G ED II
AF-S DX VR Zoom-Nikkor 55-200mm f/4-5.6G IF-ED

Price Range: $0 - $700 (for each lens not all of them)

Please only answer this if you really know what you're talking about

700$ won;t get you squat… Good lenses are not cheap and cheap lenses are just that… Cheap.

Sport photography? What kind of sports?
For american footbal you would want a NIKON AF-S 500MM 4.0 (9000$)
For tennis, you could use a 70-200 f2.8 (2400$)

For landscape you could use a 24-70 f2.8 (1600$) or a 14MM F2.8 ED AF (1700$)

For portraiture, there's actually a cheap lens worth getting: the NIKON AF-S 50MM F1.8 G (250$) and the 24-70 f2.8 mentioned above is also an excellent choice.

For events, the 24-70 f2.8 offer a nice range and good low light capabilities thanks to it's wide aperture.

Well they aren't within your price range but I would recommend the 24-70/2.8 for portraits and events, and the 70-200/2.8 for sports.

For landscape, I'm not familiar with what Nikon offers. I use a Tokina 11-16/2.8 which I would recommend. It's about 600 so it is within your price range.

Sigma and Tamron make lenses in the 24-70, 28-75 and 70-200 ranges with constant f/2.8 apertures that, combined, would stay within your overall budget.

But few people are going to suggest you buy three lenses at one time. But it's your money.