I'm still not sure If LB has mandatory KYC. As for Paxful, I believe after trading anything above 1000$ you'll have to verify your account.
For KYC exchanges, I'm not sure about the time for KYC except for Coinmama, it's less than 15 minutes. Other reputable exchanges are Coinbase, BitPanda, Bitstamp, Bitfinex, and Kraken.
I recently noticed this message on the verification tab on LBC.
Essentially, there is now a clear 1,000EUR or equivalent threshold on the amount you can trade, as well as the amount you can deposit to your LBC account before you'll be asked to upgrade to Tier 1 KYC, effective September this year. But as far as I know you are able to trade over that limit any time until that cutoff date, since I'm currently over the limit myself.
I doubt that for OP's purposes, this will be much of an issue even after the implementation of a KYC threshold, especially for a first time buyer.
preferable without all the KYC Verification or at least very QUICK registration.
It comes down to the extent of "ease" you need. All the sites with KYC are a bit hit and miss. Some people report fast approval, while others with more obscure credentials may find it difficult to get verified at all. If you're in the latter group, using localbitcoins now without these treshold in place certainly makes sense.