Honestly, most newer computers and laptops will "run" CAD "ok", though if you get into some really detailed rendering, you'll start noticing some lag, especially in 3D. Don't settle for less than 8 gigs of RAM (more is better, up to what your system can handle), a decent graphics card, and at least a dual core processor. A solid state hard drive will be fastest, but if you want to save a few bucks and have a little more capacity, go with a 7200rpm drive.
I'd also get a decent mouse. There are mice specifically designed for CAD functionality, but you can also get by ok with just a standard 5 or 6 button mouse, vs, just trying to use a really basic mouse, or (God forbid) the touchpad.
As for brands to stay away from, or best brands for the money, there are all kinds of opinions on that. I have a Dell laptop, but I got a good deal on it. Generally, they're overpriced for what you get. I think Asus is a pretty good values for the money, though not everybody agrees. Most would probably say to stay away from HP and Acer, though some of their higher end machines aren't terrible, IMO.
Personally, I like working off of a larger screen. My laptop is 17", but having external monitors (a dock station with dual screens can be REALLY nice) is also an option.
As for programs, Fusion 360 is really hard to beat for the price (free for hobbyists and startups), or if you're just doing primarily 2d CAD, draftsight is free, and pretty fully featured.