Research is the key to moving from an okay, somewhat informed TDer, to a juggernaut able to crush the windpipes of your collective opponents. To start things off, here are some of the most useful resources available. Whenever I'm in an NFL TD these sites are my ammunition:
http://nfl.com - Tons of historical data available. Need to know who had the worst passing offense in 1985? 6th round pick of the Bears in 1976? It's all there.
http://www.profootballhof.com/ - Hundreds of great players have come and gone from the game and many wouldn't even recognize their names. This site will give you a biography on every player in the HOF, why they are there, and what they accomplished sortable by franchise or position.
http://www.pro-football-reference.com/ - Now this site is stat geek heaven. If there is a stat from an NFL player anywhere, it's here. If you need a definitive answer on Brett Favre's playoff record, the completion percentage of Otto Graham in 1951, the All-Pro and Pro Bowl data from any season, or want a list of the top 100 players in career receptions, it's here.
http://www.databasefootball.com/ - similar to pro-football-reference.com. Has most of the same stats, sorted slightly differently. Good for finding team stats and rosters from any year.
(For NBA TD's use http://www.databasebasketball.com/)
(Also, be careful of http://wikipedia.org, it has its uses, but it's not the most reliable or thorough source for information. Use it with caution. Always verify.)
Here are some lessons on how to transition from "pretty good TDer" to a guy people will say "Oh, crap. I'm screwed." when they see that you are their opponent.
1. Research your opponents selections. Don't trust their stats, or their claims. Verify them for yourself. Even when they are correct, you learn to spot holes in your opponents arguments.
In this TD, when I looked up Walter Payton's stats, he had remarkably few single-season records (rushing titles, etc). I wouldn't have spotted that if I had just glazed over his picks.
2. Don't be weak, but don't be stupid either. If someone starts a TD of the Top 5 NFL players, don't just switch the order on two of them. You'll get slaughtered by the voters for having no guts.
Also, don't pick a completely different list. You'll wind up trying to argue too many things with not enough space. Pick your battles wisely, and don't be a wimp. Go out on a limb if you know you can support it.
3. Don't deal in generalities. Be specific. Give hard data. Don't say "The 1935-1945 Packers didn't throw a lot." Look up the numbers so you can say "The 1935-1945 Packers threw 250 times per season." This makes you appear much more knowledgeable and credible. This is the biggest difference between "good" and "great" arguments.
4. Have a sense of humor; don't take TD's too seriously. If you crack a few jokes and make the TD enjoyable to read, folks will give you the benefit of the doubt when the arguments are close.
5. Know what to argue. There will come a time when you will be in a TD and after looking at the numbers and the matchups, you will realize...I'm hosed. Do not give up. Shift your focus. If the raw numbers are going to kill you, don't make that your support. Focus on matchups, styles of play, and other factors. Shift the argument onto ground you CAN win. My entire third argument in this TD is an example of me doing this.
I was soundly beaten with what I had to work with. Especially on defense, and I knew it. If my opponent were not as sharp (notice he called me on it immediately) this would have worked. It still nearly did. As it is, the TD was much closer than I had any right to expect.
Veterans, feel free to post other resources you use in your TD's. Newbies-use them. If you've got no ammo, you will be gunned down by those who do.