Actually, success at the highest starting funds is easy. Do the following:
1) Hire something powerful. You don't want to lose your expedition to defending forces, and you have the funds to avoid it (most of the time).
2) Hire something smart/scary (high Int and/or Terror), ideally a Renascent.
3) Travel to a few territories with your expedition.
4) Once you've found a territory with more than 1000 in value, send an envoy to buy it. If you send a high Int unit for human defenders or a high Terror unit for monsters, then you can usually buy the territory for less than its value. Congratulations, now you have a place that is both free to visit and carries no risk! Start extracting the territory to get your money back.
So, basically just exploit the Send Envoy option to buy up most of the Colony. Once you run out of territory with positive values, you should have enough to buy up the rest. And Send Envoy doesn't generate Local Tension.
Also trade = profit. If you know how to do that, you should be ok income-wise.
Also
In this game, perhaps more than any other that I've played, sometimes the best thing to do is Rest. It is sort of counter-intuitive to most games.
However it has so many benefits!
Doing nothing allows your Merits to grow.
It also allows the fatigue of yourself to go down, the fatigue of the unit that you generally send out on expeditions to go down, and the fatigue of your companions whom you usually use for territory tasks to go down. This is vital because fatigue decreased unit abilities!
It also causes Local Tension to go down, mainly because it goes down naturally if you are not doing anything that would cause it to go up (like visit territories you don't own and maybe get into fights).
Finally, if your income is positive, then income will also go up. Trade is probably the most renewable method of positive income, as you generally milk territories dry and the territory actions only pay peanuts (remember: territory actions are balanced to keep an Outcast from getting a 100 Arkhe shelter for many, many turns, so the sums are pitiful for anyone else)
Admittedly, lower tier characters will be able to rely upon the above less and less, but its a good and simple start without giving away too much.
Please note that my giving this advice will likely lead to balance changes that may negate it, ha ha.