It depends on how I am going to use the furniture. If it is a couch or chair,
it has to be something I can sit in for the duration of an evening. I always look for support in the seat. If it is upholstered, take the seat and back cushions off and look at the construction beneath. Pick up a corner- see how dense it feels. Sit all over the couch, on each end, in the middle - lay on it! Ask to see the underside of a chair! I DO.
Give everything the wiggle test.
For a dining table/chair set, look for 'elbow room' and a table you can put your feet under with a little comfort. (No wacking of ankles under the table or tripping over chair legs that stick out.)
We have purchased both high end and clearance- price is not necessarily an indicator of quality, today.
Look for materials that are easy care and can take daily use.
I have looked online (for room or arrangement inspiration) then shopped all over- I am not a furniture snob…. I buy what pleases me- wait if I have to and save for it if need be. I am willing to look around for what I want. I must confess, I have never purchased a whole house of furniture in one fell swoop… although that sounds rather fun, if done well.
If you ARE interested in looking around, try some out of the area showrooms for inspiration, Like Ethan Allen, La-Z Boy Galleria, Restoration Hardware, Pottery Barn, Crate and Barrel, West Elm (all in or near Millennium Mall) None of those are extremely high end and you can find some decent products to fit into any budget.
Room and Board is a quality store (and one I REALLY like)- but higher end. You can check any of these places online, before you head out- and get an idea if what they offer appeals to you.
I know this may sound tedious to a single guy, 2BNTV, but consider it kind of like
buying a new car. Gotta give it some thought and do some hands on investigating.

P.S. Take along the floor plan (from your model of home) with you when you shop- and maybe a tape measure. You want to make sure that what you like will fit in the allotted space.