This character is also known as story-mode Luffy or just story Luffy (as he is obtained from and farmable from story islands). His other nickname is G2 Luffy.
Unit analysis: Due to his cheap cost and decent stats and captain ability (for the beginners at least) and the fact that you get him for free he is a staple captain in beginners teams. He is however usually considered inferior in that compared to another unit that you'll obtain early on, that is story mode Zoro, who evolves into a DEX tank captain of Roronoa Zoro Ashura Ichibugin, who will give you 2xHP bonus, through since Luffy gained his 1.5x bonus for non-STR characters, he will probably see a bit more play early in the game. Even when replaced as a captain, his stats and cost often give him a place on newbie and intermediate player STR, Fighter, Free Spirit or rainbow teams as a sub, but eventually as they acquire units with better stats/specials, he stops being useful. He is not helped by weak special, as even at MAXed stats, ~35k STR damage to one enemy will barely hurt most intermediate bosses. Therefore it is not advised to invest cotton candy in him, nor try to hard to max his levels, as he will become 100% obsolete (replaceable by better characters) after few months of play. Unless you are swimming in STR boosters, you probably should not level him up past LV 60-70.
Socket guide: don't bother, there are better Luffies out there (Monkey D. Luffy Gear Third or the farmable Nightmare Luffy Warrior of Hope), , and you should socket them first. If you don't have better Luffies and can afford to keep copies due to box space, go for the usual Bind/Despair/Matching Orbs/CD/Autoheal good choices, but really, each socket on this one is a socket you'll regret later when you inevitably will get a better Luffy.
With the release of version 6.0.1 on OPTC Global in late February 2017, this form of Luffy now has a super evolution, evolving into Monkey D. Luffy Gum-Gum Elephant Gun, who is a much better unit that can be used for some end-game content.