I've only just started using the Tekken Lord, but sweet jesus I can already see the potential is limitless. So, Heihachi mains what are your go to moves and fundamentals? --- "Man is pupil, Pain is his teacher" -Chinese Proverb
df+1 and its extensions(df+1,1 or df+1,2) are hella good. Use it when you don't know what else to do. f+4 is good for pressure, on block its +3 and it leaves your opponent in crouch. Commonly followed up by df+1 or backdash EWGF. ff+2 is a messed up launcher because its technically a safe mid launcher against some characters. Not to be abused of course due to the startup. Personal favorites for me are uf+4, which is a safe low crush and knockdown/splats and f+3 is a good knockdown/splat, also launches on CH. As for lows, db+2. This move is so cheap lol. Getting hit by 3 of these=half life and its a very hard-to-see low, +5 on hit which means you can follow up with ws1(combos into qcf+2) or ws4(4). However, if blocked, you'll eat a full launch punish. It also looks very similar to b+2 which is a mid so have fun with those. Then you have the wavedash game which is basically a mixup between Hellsweeps(although Heihachi doesn't get anything guaranteed if the 1st hits, just a mixup) and ff+3/ff+2. And of course, EWGF. Throw those out whenever you want. lol
I don't main Hei but I pair him with Devil Jin as a secondary team and he's waaaaay too fun.
Some links that may or may not be useful to you: http://www.youtube.com/watch?v=6Mi7Wdfq2wI http://rbnorway.org/heihachi-ttt2-frames/ (most people on these boards don't like to deal with frame data but I'll throw it in there anyway)
u/f+3, 4 does good damage and is safe on block. d/f+1, 2 is a good bound move to experiment with.
f+3 is also useful and can't forget about his classic 1+2 which makes a great punisher. db+2 is a great low and can be followed by 1 to catch your opponent off guard. The follow up can be punished pretty easily though so use with caution.