Thanks for all the great tips! My current run has been the most successful so far as my piloting skills improved and I became better able to fulfill contracts. After doing loads of suborbital sightseeing tours, I realized that I could get fairly close to an orbit with the rocket I had built, if I replaced the extra crew cabin with a tiny fuel tank and a poodle engine. I did so and achieved orbit easily! Then I upgrade the launch pad so I can use heavier boosters so I am now capable of ferrying science equipment and tourists into orbit (since some very profitable contracts appeared).
Aside from upgrading the launch pad, I upgraded mission control too so I could do more contracts simultaneously. I'm intending to upgrade the Astronaut complex next, for EVAs, and then the tracking station, so I can get maneuvers. After that will probably be R&D or VAB depending on which suits my needs more at the moment.
I made a working plane that was similar to the one you've got and have been able to do lower-atmosphere surveys as I went, it was a great source of income though I'm not getting much science out of it anymore. My range is still a tad limited, I think. I am getting better at landing it properly on a flat surface or even the runway.
I think I've temporarily plateaued when it comes to science. I get some point from contracts, but the other biomes on Kerbin seem to yield increasingly insignificant rewards, which I guess means I need to start looking towards something higher than LKO. I have unlocked Electrics to get solar panels, but I can't see any reason to make satellites or probes right now except maybe for testing.