like Justalonewolf said, anything smaller than a 125 will not suit you at all. They won't have the power you need and the frame will be too small for your size. I know several people who have messed themselves up good messing around on a bike that was too small. All that weight that high on a short wheel base is asking for a quick trip over the handlebars.
You should be able to get the specifications for just about any bike by going to the manufacturer's web site. Of course it will be for the current model but most of the main specifications, such as seat height, wheel base, etc. will remain the same over the years.
When you get up to the 125cc two strokes you will be in a full size bike. The suspension will handle your weight no problem. The power will be great on the flat. Hill climbs will be a challenge. Doable, but a challenge.
To get into your price range you will probably need to go 20 years old or so. There is a lot of junk out there but there are also a lot of good bikes with plenty of life left in them. Don't buy a bike that is missing a lot of parts or needs anything to be useable. Be selective and have a critical eye and you should be able to pick up a reasonable bike in that price range.
As for the brand, any of the major manufacturers should be fine. Pick your favorite color. I have a 1986 Yamaha YZ-125 and I don't have any problem getting parts. Everyday parts, like clutch/brake levers, handlebars, cables, chain, sprockets, top end rebuild kits (piston & rings) etc. I can go to almost any bike shop and buy. I can still order most of the common parts, such as chain guides, chain rollers, brake pads, fork seals, and even plastics directly from an OEM dealer, and what I can't get from an OEM dealer I have been able to find good used parts online.
I assume that you have a helmet and goggles already. You should also buy yourself a reasonable pair of boots. You can get away without boots riding a quad but they are essential for riding a dirt bike. Same with gloves. A chest protector and knee pads are also highly recommended. Remember, you can ride a quad forever and never go down, but the odds of dumping the bike are pretty close to 100%. Having the right gear will allow you to get up and keep going.
Rod