You should ask EricVol, who is an active member of VolNation, he was heavily involved in the Greek scene and a rush master at Lambda Chi. Really this kid knows a lot of people. I also know a Sigma Nu and Pike that regularly use this website that could advise you. There have been a lot of fraternities kicked off at Tennessee in the past 10 years, with KA, SAE and Kappa Sig recently coming back, so the dynamic has really changed.
There are a handful of strong fraternities, literally probably 8-10 fraternities I would join after knowing what I know and interacting a lot with different chapters. One of the biggest differences the past ten years has been the rise of Phi Sig and I am not a fan of that chapter because I believe they benefit solely due to their house, so this is hard to say. When I first started at Tennessee in 2002 they were an afterthought, then when I left in 2006 they were quickly becoming one of the top 5-6 fraternities. They had an incredibly strong rush class in 2005 and 2006 which really put them where they are now. On top of that they have the nicest house on the row (or did as of 2008, haven't been back in a few years), which use to be their only recruiting tool because they were such a medicore frat and are NOT GOOD NATIONALLY (they still are crappy nationally, that won't change). They are a strong chapter at Tennessee now and probably in the top 4, but don't judge a chapter soley by their house or you will be incredibly disappointed.
I think the top two fraternities at Tennessee historically are Sigma Chi and Pike. They are currently a lot like Bama and Florida's football teams in the SEC. It's hard to compete with them in regards to recruiting because Pike has such a strong Knoxville base (Bearden and the other elite public high school in Knoxville) while Sigma Chi gets a lot of Chattanooga private school kids and Central Tennessee guys. Sigma Chi definitely rules the roost re: private school guys and although they have a strong chapter they seem a bit of elitist, nothing wrong with that if that's what your into, just wasn't for me. Pike is great at sports and have a lot of athletes (that don't play college sports). They have a terrible reputation for hazing and I know first hand they use to haze the living crap out of their guys, not sure if they toned it down or not. I liked the guys in their chapter, just would never have pledged there due to the ridiculous hazing. SAE use to be in the same category as Pike and Sigma Chi, more similar to Sigma Chi, but has dropped a bit due to numerous probations and getting their charter revoked. SAE has typically dominated the Memphis prep school kids and also done really well with Knoxville kids. They used to have by far the most expensive fees and are also considered an elitist fraternity nationally. I actually liked SAE a lot, thought they were a diverse group of white guys, although drug use in the chapter was ramped in CERTAIN circles. I'm sure they will do well again. Back in the day SAE at Tennessee had 200 members, which was some sort of national record for any fraternity, anywhere.
Currently, the next best fraternities would be Phi Sig and FIJI. FIJI really benefitted with Memphis kids when SAE was kicked off campus for a few years. Then in no particular order SAE, Lambda Chi/ATO, Sig Ep and probably some other fraternities on the row I am forgetting, Kappa Sig is probably good again, not sure. Sig Ep was pretty big when I left but they always gave out WAYYYY too many bids which diluted their quality. You could see they were always about numbers and they didn't haze, so not many people quit and they just walked into the fraternity. I'm not a fan of hazing, but I understand why it's done and it's ridiculously hard to get rid of after becoming an instilled tradition. A lot of people consider Sig Ep guys weak and pussies for joining a frat that didn't haze. They were nice guys to me, just never really stood out in anyway.
With that being said, lots of good choices at Tennessee. Everyone has something to choose from, just ask around campus and more importantly meet the guys yourself and don't base things from hearsay. Also, DTD is terrible, so don't consider them, I think that's something a lot of people can agree about.
This is a good post ATX and very thorough. My 2 cents on top of this would be that just like college football things go in cycles with Fraternities. Probation, housing construction, bad pledge classes/leadership, can cause a good fraternity to have a few down years.
Like you said the historic best fraterinties at UTK are Pike, Sigma Chi, Fiji, Lambda Chi, Kappa Sig, SAE, and KA.
Obviously KA, SAE and Kappa Sig got kicked off in the early 2000's so they are still on the rebound (I am 4 years removed from college so they may be a lot better by now.)
Phi Sig, ATO and Sig Ep all were really good while I was in school and were right up there with Fiji, Sig Chi, Pike and my fraternity LXA. (we had some down years when I first joined, my brother was an LXA as well in the late 90's early 2000's)
Anyway, I agree with what someone earlier said about joining the fraternity you fit in best. Pick about 10 to start with and check them out and narrow it down to 2 or 3 really quick so you make sure you spend enough time at the houses to get a bid.
I personally am so glad I joined a fraternity. I have plenty of friends that came to UT from my high school (DB) and could have just rode that train all through college. But I wanted to branch out and meet new people and the greek community provided a great network of people. I also made tons of other friends throughout campus so anyone that tells you, that you will be secluded to greeks is wrong.
I come back to Knoxville every gameday that I attend and meet up with any of my old fraternity brothers that are in town, we tailgate together and go to the fraternity house every gameday and we are still welcomed with open arms, it really is a lifelong brotherhood.
Don't worry about the people that say you pay for your friends, any club charges membership dues, even in the adult world. The money goes to maintaining the fraternity house, parties with awesome bands, bus trips to away games, and insurance to nationals and the University. You are not paying for your friends.
Most fraternity houses are very affordable living situations with inexpensive meal plans. You can pay your fraternity dues, live in the fraternity house, and have a meal plan for much less than living in an off campus apartment and paying for all your meals off campus.
Anyway sorry for rambling, good luck and I am jealous!