As we know, one of the major sources of information in the AlphaBay bust was Bitcoin. LE is capable of following it. DO NOT USE IT.
Use an anonymous coin. The only one in real use is Monero afaik. It's untraceable. Use it!
With all it's drawbacks, I liked AB because it had Monero support. Not sure if any of the markets out there support it. If you want to use a market that has only Bitcoin support, use a just-in-time converter such as shapeshift.io or xmr.to
I had good experiences with both, but the latter has an onion address and claims to wipe logs.
OPSEC: Buy your bitcoin anonymously. It doesn't matter if the blockchain is public if the people you buy and sell from don't know who you are or have any way to contact you.