I recommend checking the bottom of any asparagus you're thinking of buying. The moister they are, the more recently they've been cut. I also try and feel the bottom inch or so; if it feels tough and fibrous, it was likely cut a while ago. And, as Son recommended, look at the tips. Don't buy any tips that are slimy, or soft - look for tips that are solid. (You can also cut the bottom inch plus or so, then peel the outer layer of the lower portion of asparagus until you get past the tougher, fibrous outer area and use the remainder. You may still have a little fibrous portion of the base, but you'll also have more usable product.)
As for thickness, I prefer thicker spears now because my favorite way of cooking them is on the grill (brushed with a little oil and salt and pepper, and over direct heat until just sightly charred), or in a hot cast iron pan with the same preparation. Thinner spears tend to wilt too much when cooking at such high heat.
And, instead of a dedicated asparagus cooking pot, I get a pot of salted, boiling water going, hold the bunch of asparagus by the tips, and then submerge the bottom portion (two inches or so) of the bunch in boiling water for about 2 minutes and then drop the entire stalks into the pot. That way, I get the stem partially cooked before cooking the delicate tips.