I play on peaceful all the time anyway - hostile mobs just irritate me. With regards to starting out, my general tactic is:
1: Gather wood, make wooden axe, gather more wood until axe breaks.
2: Make wooden pick, gather stone until pick breaks.
3: Make stone picks, search for and gather coal.
4: Search for and gather iron, make iron picks.
5: Search for and gather diamonds, make diamond tools.
6: Search for whatever materials I need for whatever I plan to build.
Finding coal early is vital, unless you just want to sit on your hands and wait out the nights. I also tend to build my base near the spawn point, so that the compass will lead me more or less home.
This is what I generally do when I start, though step number 5 is usually not a priority considering how rare diamond is. I will dig down far, and if I do find some I cry with joy and if I don't, I just keep on digging. I do most of my digging during the night, when I don't feel like running from the skeletons, spiders, and creepers.
Has anyone here encountered Slime? It's a creature that spawns near the bedrock, is not hostile and will drop a green goo ball when killed. They resemble a square head that bounces around. They are extremely rare, and will also spawn in the light if you have torches around. I've been keeping an eye out for them, even though they are pointless at this point of development (their goo doesn't do anything yet). Only heard about them via the official minecraft forums.
Also, in order for me to take down my hill next to my castle I have employed Creepers. When I say employ, I mean I lure them to the top of my hill and allow them to get close enough to start their detonation process, where I promptly run to a safe(ish) distance. Works wonders, I mainly do it during the early morning when the other monsters have burned up and they haven't despawned yet.