With my own kingdom I've got 4 castles and a city for myself, all garrisoned with 200-400 men each. My current troop wages are a little under 50K per week, which through investments and taxes gets knocked down to ~11K. You can easily make more than that just by doing a trade run or two, or by taking on the larger roaming parties and selling loot/prisoners.
So that gives you an idea of how much you should aim to be pulling in a week. I had around 200K when I split.
I know you were advised earlier against joining a faction as a vassal, but I would encourage it. You don't have to follow the marshall. So long as you report in to the initial summons, you can go off and do your own thing afterward. Being in a faction will give you more chances to take on other lords, allowing you to get easy honor/faction (by letting them go) or cash (through ransom). I'd recommend letting them go until you have your own kingdom and it becomes your own lands they threaten.
Eventually you'll be offered the marshall position, and you should take it. You can use that faction's other lords to help you establish your own kingdom by capturing and requesting a castle or city. If you're granted the castle/city, than great. Use it as a source of revenue, and start stockpiling troops. Keep taking castles/cities and always request they are given to you. Eventually you wont get one, at which point you can rebel and keep all your other lands that the other lords helped you get.
You'll start your kingdom with a good build up of troops, a source of revenue from the castles, and once you are engaged in a war with another kingdom, you'll have spare villages to grant to any lords who you convert to your side which will let them field larger armies.
As a side note, when you're in a faction as marshall, you should attack lands close together so that when you split off, your lands are easily defensible. You don't want to be a new king without support and having to travel across the map to defend different locations.