Easy money in Kerbal Space Program
Your desires are not compatible.
The entire point of using the contract system in the first place is to add additional challenge to your game, and to structure your space program.
Since you appear to have a very clear idea of what you want to do, and don't appreciate the additional constraints and challenges that come with the contract system, the best thing to do is to not use it.
If you absolutely want to use the contract system, the trick to earning oodles of money is to launch missions that cost far less than they bring in, and using the time between mission events to launch additional missions.
For instance, in the time it takes you to do a Minmus round trip, you can fire off a dozen missions to the Mün, and in so doing make available further Minmus contracts, meaning that the initial cheap mission is made even more profitable by later developments.
Side note: A TWR greater than 5 is almost always a massive waste of money: Unless you absolutely, positively need to get into space immediately you're going to burn most of your fuel fighting needlessly against the atmosphere, and even more in way too steep an ascent.
Put some satellites in orbit on nearby bodies with a science device and antenna and accept the "send science from orbit around X" missions. You can just switch to the satellite and do the science and transmit.
You'll have to change how you generate cash as you progress though the game and the available Contracts change. Usually by about the time you are shooting for the moons of Jool and have unlocked 75% of the science tree, you should have more than enough money to build any kind of monster spaceship you want.
Farming part test contracts are you best path to early game cash. Contracts requiring only Landed on Kerbin are pretty much free money. Accept a few and and stick the parts on a MK1 Command Pod, run the tests on the launch pad, and then recover. Sub-orbitals are the next best thing. The key is to strap as many parts with similar test conditions to a simple craft as possible. Usually just a single BACC SRB launching the parts attached to a command pod is enough.
These missions are simple and take less than 10 minutes to construct and fly. You don't even need to fuel a rocket part to test it successfully. Use these contract missions to fund the more interesting ones.
Once you start sending manned missions to other planets, you'll need to switch to using probes to generate your money. The easy part based contracts will generally dry up at this point. A small probe can do the trick of satisfying the full conditions of a exploration contract( reach orbit, transmit science from orbit, and transmit science from surface). And it will do it quicker and cheaper than a manned mission. You usually only need to get a LV-N with a Fl-T800 fuel tank into orbit to have enough delta-V for a probe to reach any body in the system(provided optimal orbits). You'll essentially be using probes to fund and acquire the science/parts to make the followup manned mission possible.
Other than that, keeping Kerbels on other planets and in orbit around Kerbin is also very useful for quick cash. Having someone available to plant a quick flag, or rescue a stranded Kerbal from orbit is a great return on investment. Both of those tasks tend to have high cash rewards.