It doesn't matter when you use the star-lit crystals, though personally I tend to wait until a weapon is fully developed before putting any upgrades on it (so I'm sure I'm not going to trash it due to bad legacies or whatever).
Each crystal gives you a small increase in DPS and other stat/legacy ratings on a LI. Note that any value that is a percentage, cooldown or pulse count (so most legacies actually) is NOT a rating and not affected by crystal upgrades, and the increases are really small (like +1 in dps or +4 crit rating, barely noticable). Personally I'd never spend TP for them.
Used to play: 85 Champ / Captain / Runekeeper / Guardian, Guild Master of everything but cooking.
Playing now: Hellcat / King Tiger / GW Panther / IS / KV-5 / M4 Sherman and more