I’ve owned all three, and without a doubt the Toshiba’s have been the sturdiest and most reliable. I can’t even speak about their tech support line, because I’ve never had to call it. (I’m typing this on my current laptop, a Toshiba Satellite Pro.)
Not so with Dell and Gateway. Admittedly, of the two, if you simply must have one of them, I’d recommend Dell over Gateway, based solely on personal experience and those of friends and coworkers.
Gateway is by far the worst of the three. I had to have the LCD replaced twice (though I suspect it wasn’t replaced at all the first time it was sent in); the CD-ROM drive blew something and spun the disc at full speed, incessantly, all the while returning read errors; the battery sucked ass from day one and they refused to replace it (I was only getting about 45 minutes from a full charge!); and finally, I lost everything when the drive went kaput. All of this within the warranty period, and all of it a pain in the ass to get handled.
The Dell was better. Their service is… well, it left something to be desired, but the hardware essentially worked as advertised. I had a power supply problem, which turned out to be a faulty adapter, rather than the laptop. However, they reloaded the laptop anyway, which meant I lost everything and had to reinstall a bunch of stuff. That was annoying, but at least it was fixed. I had a few problems with their bundled software, but I got rid of all that junk (which I recommend doing on any new computer, anyway). The laptop lasted for about a month past the 1-year warranty, then stuff just started dying. I traded it to a local shop in exchange for some parts for my desktop machine.
We’d been using Toshibas at work for a while, in some pretty extreme conditions at times (construction sites, a wood-pulp plant, a water treatment plant, etc) and aside from cosmetic damage all of them were holding up well. In fact, when work decided to upgrade I took the opportunity to buy one of them myself, and it still works to this day – it’s a Toshiba Satellite 115CS, running a whopping 24 MB RAM and a smokin’ Pentium 120 processor, but it still works, after several years of hard use in the field. It’s at least 10 years old at this point, because they had the laptops when I started working there in '97.
My current laptop is about two or three years old (it sat in the warehouse for who knows how long before I got my mitts on it) and is doing just fine. I love it. It’s been on vacation with me, to the ocean, on camping trips, to work, you name it. For a while I used it as an oversided iPod (via a tape adapter and my car stereo). I use it to play DVDs because it’s got a better picture than my home TV. And not once have I had to call tech support, for anything. Everything just worked, out of the box.
I love Toshiba.
ETA: my current machine meets most of your stated requirements, falling a bit short in processor speed, and only cost me a little over $800. Not a bad deal at all.