My new computer should be arriving in the next couple days, I want to take my old Gateway down to the master bedroom just to be able to keep some pictures and files and to occasionally browse the internet.
I'm guessing I'll need a wireless router for that purpose. The master bedroom is downstairs approx. 125 ft away from the upstairs office.
I'm looking at getting a D-Link DIR-655 Extreme N Wireless Router with a D-Link DWA-140 RangeBooster Draft 802.11n N Wireless USB Adapter from Amazon.
I have no idea if this would be the right type of gear for the uses I want. Any ideas or suggestions on equipment to just enable myself to get our second computer online would be appreciated.

You pretty much have it. The 'N' wireless isn't needed for your uses, except that it offers better range, this is the only reason I have a "N" router. I run "G" cards in all my PC's and the router set for B&G only. I get great reception through out my house with the 'N' router. My old wrt54G router just didn't have the range to reach the 2nd floor from the basement nor a corner of the kitchen, even with booster antennas. You should be up and streaming pictures in no time.

Just follow the installation instructions for both and you should be fine, it isn't hard to set them up. Once it is working or at least arrives, post up what ever questions you may have.

I'm also running a D-Link DIR-655 Extreme N Wireless Router, love it, works flawlessly, very easy install, even for an old guy like me.

It's set up on the second story of the house in a room that has a lot of ductwork under the floor so I was concerned that this might not be the best location for me but there have been no problems, conplete coverage from the top of the house to the basement. I have also taken my iPod about 100+ feet outside the house before the signal dropped away.

Is the 125' distance a straight line guesstimate? I am wondering if you do need the rangebooster but better safe than sorry as you are going quite a distance.

I am agreeing with the question about the distance. 125' is a 12 story building straight up. Granted, you might be going at an angle, but it seems a bit far. You might be just fine without the range booster.

I remember a guy that asked me about a similar thing a few years back, and he estimated his distance by measuring (with a tape measure) the path he took when WALKING from the computer to the router. When I told him that this is wireless and the signal goes through walls, he said that he knew that, but since he was going between floors, he had to find a way for the signal to get through the ceiling. Doh!

Thanks everyone for the replies, I went with the equipment I listed, even at an angle the distance is over 100ft, I figure it's better to be safe than sorry.

You can use powerline ethernet adapters. Use your AC wiring to run wired ethernet. I use it in my house. Netgear (XE103 and XE104G) and Dlink make 'em.

Experience with Netgear's desktop switches has led me to swear off them in toto. I'd take D-Link over Netgear for sure -- my DGS-2208 UTP switches work great.