The supply question having been covered excellently by Kahuna, I'll focus on scouting.
TL;DR version: send a big old blob of scouts and scrap all but 1 survivor once they're safely in the target system.
I use the "cheap" way of scouting, unlocking scout starship mark IV at 1 second into the game and using it to scout the entire galaxy because it has tachyon immunity.
Barring this method (which eats 7500 of your initial research) it becomes important to understand what cloaking boosters are.
1) cloaking boosters are fired by 1 cloaked ship at a nearby cloaked ship and basically "absorb" the first detection that would hit the boosted ship, allowing it to remain cloaked.
2) A ship firing a cloaking booster cannot itself receive a cloaking boost.
in practice, this means that if you send 4 scouts, a,b,c,and d out.. a boosts c and b boosts d. first tachyon gaurdian, a and b get decloaked, others remain hidden as they speed past. A and B probably die. c begins boosting D. second tachyon your scout hit, c gets decloaked, D slips past without being detected.
so.. 4 scouts mark I to pass 2 tachyon detectors. since there is 1 tachyon unit on each side of a wormhole, it takes 4 scouts for 1 jump deep (assuming you sent fighters to clear tachyons immediately adjacent to you)
since it takes 4 times as many per jump if using mark 1, and mark 1 has a 10 ship cap.. you pretty much have to unlock mark 2 or use transports for anything past this. since mark 2 has more than 1 cloaking booster, the math gets messy and I'm not going there in this post. Thus, the TL;DR version above is my advice.
personal sidenote: apparently my fingers think the proper spelling of tachyon is "tachyone", I had to go correct every instance of that word in this post. bad fingers, bad!