Ok, so I've been playing the game for a while now, and got a pretty solid grasp on things and mechanics, but not to the point of minmaxing yet.
I've tried to run things 2 ways mostly. I've made it to day 14 getting 500 rep with all 4 guilds by changing the quests on day 7 to medium difficulty and running bandit dungeons and farming some slaves from those, either for gold or personnel. My start is always the same:
1st slave: Dark Elf. Apprentice (Druid-Caster-Necromancer). You build your Master to be your nuker early on, and since you have to worry about training high wits ASAP, I'd recommend buying a slave that can benefit from wits early on aswell, either a second magic user or a worker, to spend the first day building up your wits with that slave.
Side with fighters. Don't sell anything you can use yet, we're not in a rush. Unless it is for an improvement, or an extremely good slave.
2nd slave: Seraph (Fighter-Valkyrie-Knight) or another high health race. I like Seraphs for the sole fact that you can get holy lance by day 4 to 5 by doing physical training, and that allows you to snipe those bandit assasins and make your day7+ runs much smoother.
3rd slave: Worker/2nd Nuker, whatever is available with high wits. This slave will have to be your lockpicker/fisher early on, so make sure you spend that first day training your wits with it.
The first couple of days are just goblin runs. Demolish stone shrines, ignore others, lockpick with your 3rd slave, and just keep using your social skills building up obedience/loyalty. Once you're confident your team can take on bandit dens, you go and start farming slaves. I usually get there by day 3 or 4, depending on the first golbin runs and the gear i have with me.
What's important to have in mind is that demolishing shrines gives you a lot of stones/obsidian early on that can make a difference by the time you get to hour 23 and want to go to the shop and trade for food/gear before the reset happens at 0hs.
Make sure you rush your rooms to expand towards making a second team to run in parallel with your main team, either by splitting the first team or starting one from scratch with a good tank. With good medium armor you can get away with a single slave frontlining and healing after combat. But things need to die for your lone frontie to stay alive through the entirety of the combat.
Use your hours wisely. You'll mostly be using them to travel to your dungeons, don't rush things.
Keep in mind always that you'll need to train every day with a slave. At the moment, there's only one interaction available per day and getting wits+charm maxed on your master should always be a priority, so that by day 7 you can make the most out of the medium difficulty quests you'll get.
There are no hard quests, just some that take longer. If an item requested is not in the market, you can always look for it elsewhere.
Slaves come and go, so long as it's not one from your main team, they can be replaced, and even those in the main team can too.
You can also spend an extra couple of days grinding on a single slave to meet the requirements for a quest, it's fine so long as you remember to multitask and not rush to the next day to complete the training. If you don't rush your hours, you'll get to day 14 with 500+ rep on at least 3 guilds AND 1k+ gold.
If you would like me to expand on this I'd be happy to document a run and post it somewhere.