What is the order to do things in KSP career mode?

[Harryambe]

I have managed to do my first orbit on Kerbin and return. My next 'mission' is to fly near Mun. However I am a little lost with what I should be doing to start getting more money and science in a smart order.

Do I want to start putting satellites up for science transfer? (If that is how they work). Do I keep sending out ships with experiments and try go to a different location each time?

[TimTheEvoker]

Have you created a rover or something of the like to harvest the rich bounty of different biomes that is the Space Center itself?

[Eventide]

Rewards increase with the distance of discoveries; More science points are earned from the far planets than nearby ones. Your last point is spot on, just difficult to achieve with the most distant planets early on, where the intercepts get complicated. You can fill out a good chunk of the tech tree running back and forth to Mun and Minimus.

Simply escaping Kerbin's orbit, to the Sun with an overpowered simple rocket (unmanned) and some science gear will net you some fairly easy points early on. Automatic milestone reward for getting out there, with no destination in mind.

Take satellite contracts; do part tests - some are quick and easy.

Unlock science parts to get more experiment options and science points from that, perhaps even as a priority over bigger rocketry parts early on.

[JBrown247]

I do a bunch of the tourist contracts that are Earth orbit before going to the Mun. I think if you go to the Mun, the tourist contracts will require you taking them to the Mun, which isn't idea.

It is boring, but if you grind the tourist contracts at that point, you can upgrade all of your base.

[Aaron]

I like supplying/repairing/delivering sattelites for big money

[bUrnIt]

Hi,
Let me contribute those planes (1 SSTO)

for your LKO crew recovery, LKO tourist. Advanced to Pro.
https://steamcommunity.com/sharedfiles/filedetails/?id=1760970836

for your GROUND & AIR missions on a small fuel tank: very sturdy 4x speed mini jet.
https://steamcommunity.com/sharedfiles/filedetails/?id=1584278093

attention: May need to tweak a little the tails flaps maybe for take off and landing. (on the fly, and you make it sturdier again for faster speeds)

[Drosta]

Just don't do the airplane based missions if your goal is optimized career progression. They are usually slow as they require precise waypoints often very far away on kerbin from your launch site. And I dont know if this is still a thing. But transmitted science is worth less than directly collected and returned science. So check into that and keep it in mind.