The Most Logical Thing to Do on the First Day Is...

[kuribo]

Tunnel the first person to suspect you

[kuribo]

I don't really know since I've never played Mafia before (but I have read through two games so I understand the rules), but I think the best thing to do on day 1 is to vote to lynch one of the lurkers (unless, of course, both you and the lurker are scum). Even if they were a townie or someone important like a cop or doctor, they're not helping the town if they're keeping their mouth shut. It can also make them look suspicious.

You must give them a chance to say something before you decide to lynch them, though. If they don't say anything, or accidentally reveal that they're scum, vote for them to be lynched.

However, you should only do this if you have no ideas whatsoever on who has what role. You should probably question others to see their reasons behind things. But like I said in my first sentence, I've never played any games, so I don't know for certain.

(Edit: Just looked through a game on here, and it made me realise that the first day can last long enough for people to get plenty of reads. So, I added more to my answer.)

I think you should play. Do you need a mentor? Can I mold you into my own image?

[kuribo]

If you're both interested, I'll need you to fill out the standard application, followed by the personality test and the physical challenge. After that, the two of you will need to fight to the death within a steel orb at the bottom of the sea. Once my successor has been chosen, training will begin in the following areas:

Murdering your friends for fun and profit
Bussing: why you should stand alone on the bones of your scum team
THATS IT FUCKER ITS YOU OR ME: a philosophical discussion of what to do when one person votes you
Rage quitting
An extensive psychotherapy regimen under the Serene protocols

[kuribo]

Only if you take the placement test or you've completed Comprehensive Dick Punching 101