SilkforCalde gave you the best advice in this thread.
I rarely make PuGs myself, but luckily most "Alts of experienced raiders" who do so all know me and my alts, so I usually get spots pretty easily in whatever raids there are going on.
Anyways, the few times I've made PuGs here's what I've done:
1. Ask around "brained" raiding-guilds. Just go /who Guild-X and ask them if there are any raider-alts interested in your run. Our realm is luckily quite small so I have 1-2 persons from each good raiding-guild in my flist/real-ID so that makes this quite easy.
2. Inspect everyone, preferably even the "alts of experienced raiders". If it's someone I know that is exceptional I'd invite them for BWD/BoT/Tot4W even with ilvl346 equipped. Even a few pieces of PvP-gear is acceptable as for most classes 2/4-set of Ruthless/Vicious gear outclasses 359 gear quite easily. Gear is honestly not such a big issue as long as they're not in all-blues/greens.
3. As stated before, if you end up inviting some real randoms, make sure you inspect them and double-check their achievements from the Armory. Or just ask them some crucial questions about boss-mechanics and such.
Dont be a clueless raidleader who goes "ACHI AND ILVL NO INVITE!" or "Y HAS 2 PVP ITEMS NO INVITE LOL NUB".