First Time Dallas Visit!
It's unclear just what you're looking for, and where you are staying and whether you'll have a car makes a difference, but I'll take a shot.
As far as things to take home, I'd first go to Central Market and get some Texas salsas, hot sauces, chips, beer, wines, and other goodies (they have a helpful staff, just ask). CM makes good tamales, get some of those. CM also sells local cheeses by the Mozzarella Company, but if you go to their store in Deep Ellum, there's a better selection. If you can take home perishables, just down the street from Mozz Co is Rudolph's, a butcher shop that makes their own, great sausages. Likewise, Kuby's, in Snider Plaza, makes incredible German wursts; and Jimmy's Food Store makes wonderful Italian sausages and meatballs. Jimmy's also has a small section of locally made pickles, sauces, etc. You should have a sandwich at Jimmy's in any case; it may well be the best meal you have in Texas.
Most folks from the great frozen north think of barbeque and Mexican food when they think of Texas. Dallas doesn't have great barbeque, but we've got some pretty good stuff -- try Pecan Lodge in the Farmer's Market (Shed 2, Thurs - Sun only), or Lockhart Smokehouse in Oak Cliff.
You also need to have a real taco (e.g., baracoa, al pastor, lingua), and not at some white-bread place. Try Taqueria El Si Hay in Oak Cliff or the spot at Fuel City (yes, its in a giant truck stop with longhorn cattle). For real Mexican cuisine (not Tex-Mex) go to Komali or, in Oak Cliff, Mesa or Vera Cruz. There are a ton of Tex-Mex places: El Fenix, Mia's, Herrera's, Avila's, Manny's Uptown, Nuevo Leon, Mi Cocina, Chuy's, I could go on and on.
For a good, down-home breakfast with a side of biscuits and gravy, go to the Original Market Diner on Harry Hines Blvd or John's Cafe on Greenville Ave. Just good, hearty greasy spoons.
Should you want to try Southern soul food, go to the South Dallas Cafe or Sweet Georgia Brown's.
For upscale southern cooking, go to Hattie's in Oak Cliff or the Screen Door in the Arts District.
For fancy restaurants, there are any number of threads on this board to guide you.
Welcome to Dallas.