Skirts (and jackets, if jackets float yer boat), in neutral solid colors like navy blue, beige, gray, black. Not white, because it shows every ballpoint pen mark and dust smudge. Slacks ditto.
If you can find skirts that have pockets, they will rule. Every so often you just need to stick something in your pocket (keys, kleenex, item confiscated from subordinate), and if you have a pocket in your skirt to stash that employee ID card you just found on the floor while you walk past all of them until you can get back to your office and look it up to see who lost theirs, you will bow low and bless the skirt’s designer.
Hemline: here mileage will vary wildly. Personally I prefer a career woman’s hemline to be at, or just below, her knee (yes, I am your Mom 
). This is a flattering length, and it avoids you having to constantly be tugging your skirt down every time you sit down in a chair. It also sends a “I’m a serious person” signal in my opinion, because, let’s face it, male co-workers ARE going to be looking at your legs, and a businesslike, modest hemline will encourage their attention to remain on task. Higher hemlines tend to signal “I’m interested”, so do your purchasing and hemming accordingly.
Blouses, shirts, turtlenecks, can be white or in brighter colors, to jazz things up so you don’t look like Miss Navy Blue 2008. Also look for pretty prints.
No see-through. And also, in my very humble opinion, also no exposed bra straps, even athletic bras. My daughters and I have had to agree to disagree on this issue, but I’m old-fashioned, and exposed bra straps make me uncomfortable. So it’s a pretty sure bet that where you’re going, there will be other Fifty-somethings who will also be made uncomfortable by exposed bra straps.
And along those lines, personally I’d always wear a slip so the outline of the bra isn’t revealed. Again, I’ve had to disagree with Young People Nowadays on the idea of the colored bra as just another fashion accessory, meant to be seen through the blouse.
Conservative heels, by which I mean “librarian heels”. If it’s got a spike, it’s the wrong pair. Depending on how much walking you’re going to do during the day, you’ll want a lower heel for more walking, or even flats. IMHO good-quality leather shoes send a better message than Payless Plastic.
Ditto pocketbook: good quality, not too huge, businesslike. Personally I like zippered compartments and lots of 'em, because that way when you’re running for an elevator and you slip and fall on your ass, all your junque doesn’t go flying out all over the floor from your overloaded open bag.
Regarding shoes and purse, I always remember Hannibal Lecter’s scathing remark to Clarisse Starling about her “cheap shoes and good purse”, meaning she spent money on things people would see, like her purse, but skimped on the things she didn’t thing anybody would ever notice. But of course, he noticed; she should have spent the money on good shoes, because they’ll last a long time and you need them to be comfortable, but a purse is just a fashion accesory.
Minimal jewelry–small earrings, tasteful gold chain (one). Personally I’d eschew the huge dingle-dangle earrings. They may complement your jawline and look dynamite, but they send a Teen Wannabe message IMO, not commensurate with your supervisory position. Big earrings also make it difficult to hold a phone against your shoulder.
Sweater, in case your office keeps the thermostat at 70. Make it a simple cardigan in a neutral “goes with anything” color, like navy blue or black. Good luck finding one, you may have to shop online.
In my experience, Wal-Mart is useless for “career woman” type clothes; they tend to major in up-to-the-minute teen-oriented Fashion with a capital F. You’ll be better off at stores like Target, Kohl’s, Sears, and JC Penneys.
White pantyhose will make your legs look fat. Just sayin’.
ETA: Your office doesn’t have A/C? To stay cool, you’ll have to wear cotton. Nothing but cotton, and linen, too. No polyester, if you can help it.
I just had to rant; I used to have a coworker that would wear electric blue bras under white shirts. :dubious:
