Monero - You can't go wrong with. King of Privacy and will be for a while.
Verge - Meh, don't trust the developers and they barely just released stealth. I only ever see people investing in Verge to try and make money, not use it for privacy.
DeepOnion - all hype/marketing, no tech. I feel like the only reason they have such a large community was because of the airdrop program. Concerning when it ends.

Another coin to check out would be Spectrecoin (XSPEC). Its got Tor, OBFS4 so it works in Tor blocked places like China & Iran, ring signatures, fast speeds, and its a Proof of Stake coin so you get a 5% yearly return on your coins if you're staking them. The 2.0 release for XSPEC is going to make stealth addresses default (right now they're optional) and introduce Stealth Staking. People don't think Stealth Staking is possible, so it could be a good investment if you get in before its implemented in Q2 2018. Feel free to join the slack and talk to the developers and do your own research.

So basically, I'd go with Monero if you're looking for something that works well RIGHT NOW. Should definitely look into XSPEC though.