Dockers makes a decent chino. You can shop around at a local department store and find something, I’m sure. In terms of color, I’d go for a darker khaki, a pair that’s light gray, and something in navy. Nothing that’s pleated. Since anything in chino cloth is on the lower rung of business casual already, I’d avoid a product that incorporates too many casual styling elements. Dockers’ “Alpha Khaki” is the kind of pants that step just over the business casual line, and they come off as too comfortable and too jeans-like.
Choose a cut that flatters your shape. Avoid classic or relaxed fits. You don’t want a sheet of fabric billowing around your thighs, but neither do you want something that clings to your legs. Try to find a nice slim-straight cut, or maybe even a straight. It depends entirely on your body shape.
The type of shirting you choose will depend largely on your shape. You want a tail that can be tucked comfortably. Unless your proportions are quite generous, you might try looking for shirts that are darted (or even double-darted in the back). Again, avoid classic or relaxed fits. You don’t want excess fabric wafting around your waist. A clean tuck is very important. No outrageous patterns or colors. Oxfords are nice. Nothing that has a sheen to it. Broadcloth is a good fabric, but it can have a shine.
Do you already have a jacket, as a part of a suit that you already own? You might be able to re-purpose it, depending on the style and fabric and color. Unless it’s seriously formal, you probably can.
Otherwise, I’d recommend getting a nice gray jacket. Preferably tweed, and maybe herringbone, if you can find it. I know that you said that you were looking for a navy blazer because they can go with anything, but a gray jacket (provided that it’s neither too light nor too dark) will coordinate even better than a navy jacket. It also looks better, IMO.
If you’re buying a tie, don’t buy any ridiculous patterns. Try to avoid a tie that’s too wide, but most of them will be. Don’t buy a tie that’s too narrow, either. I know that’s not great advice. I think 2 1/2 inches at the widest point is just about the perfect size for a tie. You can go a little slimmer, but I wouldn’t go much wider.
You can find most of this stuff in a department store. I’d recommend J. Crew, but I know you’re on a budget. I asked your age because ordinarily I might recommend something like H&M, who make fashionable, well-fitting clothes that work well inside a business casual setting. Their target consumer is a little younger, however. Maybe it wouldn’t hurt to look around, though.