Wow, I haven't touched 8mm film since 1996. Phew.
You might still be able to find a service that transfers "home movies" to VHS or DVD, but they're disappearing if not gone entirely.
Professionally, you could search a bit more for a telecine transfer facility or an optical house. A telecine transfer facility could probably handle 8mm, but the older reels may not get the special handling they'll need (hopefully none of your reels snap, crack or break just because they're brittle with age). Film scanning is usually done with Super 16 or 35mm. I'm not sure you will find anyone who can scan 8mm. And, even if you found an optical house that could do it, the cost per frame might be over your budget.
I think you've made the best decision to do it yourself.
You have a projector, correct? And, a room where you can project the picture onto a white wall or screen and control the ambient lighting at the same time?
In film school, we just projected the film onto a wall and shot the projected image with a video camera. The video camera should be as close to the projector as possible to minimize any perspective that might get introduced because the projected image and the recording device will have to be slightly off angle. If you happen to have a large enough space, you could experiment with projecting onto a sheet, shooting the projected image from the other side of the sheet. This will flop your image, but that can be easily reversed in most video editing software applications (Final Cut Pro and Premiere Pro for sure).
I'd usually recommend a DVCProHD camcorder for something like this, but those start at $6,000.
I've always liked the Canon HV series. The current model is the Canon HV40 (should be around $800), but you can probably find the older HV30 at some retailers for less. It records HDV and MiniDV. I'd recommend shooting in HDV mode, framing your 8mm picture to your liking as you record to a 16x9 HD format. What's great about this camcorder is that it allows you to turn the automatic features off, which you'll want. Most likely you will want manual focus and manual exposure.
By bumping your 8mm to HDV, you're pretty much going to the 2010 equivalent of 8mm film in 1939. Your reels were probably shot on 8mm rather than 16mm or 35mm as a cost consideration. Today, one might pick HDV rather than XDCAM HD, DVCProHD, and HDCAM as a cost consideration.
You'll want to capture your HDV footage, clean it up (probably slight image correction using levels, curves, and b&w and/or color adjustments) and then export HDV masters of your footage. Once you have your HDV master clips, these can be archived back to tape or other storage media (requiring about 3.6Mb per minute) as well as transcoded for web video, Blu-Ray, DVD-Video, MP4, etc.
Report back on what you finally do on this!