I can remember my first business trip and my big oversized red suitcase with no wheels. But, that was a long time ago. Don't worry. I have plenty of suggestions for you. First rule of business travel is to have one roller bag and one tote so you don’t have to check a bag. A professional looking tote (leather or vinyl) is perfect to stash your laptop, power cords, and a small crossbody bag to hold your wallet, phone, make-up, keys and whatever. That way you can secure the big tote and just grab the crossbody when you are going to lunch or dinner. You can find great looking ones for a steal at Target (my daughter has one and it looks well made and expensive).
As for your wardrobe, my suggestions may already be in your closet, or you can purchase pieces at H&M, Target, Ann Taylor Loft, The Gap, Old Navy or Banana Republic depending on your budget. These are foundation pieces you can wear again and again. For travel, wear jeans, a solid t-shirt, cardigan and ballet flats or boots depending on season. For day one, I'd go with a sheath dress or a pencil skirt in navy or black paired with a crisp button-down shirt and a short jacket. Any color, even a denim jacket in olive would look great. Roll up the sleeves a turn or two, add a statement necklace from Forever 21 (or wherever) and put on a pair of pumps and you have a classic yet contemporary look that can go from your client meeting to dinner. Just make sure you can sit down in the skirt and watch the panty lines.
For day two, go with a pair of black or navy pants paired with a silky/poly-blend button-down and a cardigan. Add simple silver or gold jewelry and wear either the pumps or flats. If you're headed home after work that's a comfortable way to travel. If not, it's great for dinner, or if you're looking for a more casual look, throw on a pair of boyfriend jeans.
When I travel I admit, I take an extra top or bottom just in case I change my mind. But, don't over do it. Dragging a heavy bag around isn't fun. There are two must-haves I don't leave home without. One is a lint roller for my dark clothes. The other is a $1.50 shoe shine sponge to make old shoes look brand new. Both can be found at Target or your drug store.
Have a great trip! You're going to look professional and absolutely amazing.