The main thing when choosing a wand is to make sure the jets don't point straight down to the carpet. That's a "no-no". You want a 2" tube. More jets means you can get the jets closer to the fiber for less heat loss and steam. Jetting of .10/12 flow is a good place to be, to have a higher flow wand that is. Higher flow means you can get more water to the carpet for faster rinsing without increasing the pressure so that you don't wet the backing (high pressure is what wets the backing), angled jets help with also.
I don't know if you can get a greenhorn wand anymore, but in my opinion it's the best bang for your buck wand. The wands mentioned above are all probably better than a base 2 jet wand. Of course if you want a wand that will last you a lifetime then get a Titanium.
A good recommendation for the best cleaning method would be a RV 360i or the like like mentioned above. Or you could go with the 175 floor machine with pad/brush to scrub in your preconditioner, rinse with your new high flow wand. It was the board recommendation for heavy soiled carpet, before the 360i was made famous by our fearless leader. I've never used a 175 but I've used a cimex to scrub, and a pad driver on my RX. Now that I've jetted my rx to 6 flow with flat jets and I'm using it again. I have to say that there is a difference. The carpet seems slightly more damp but the carpet is cleaner and it seems like I'm getting more referrals.