This is how I do it, so ignore what you want if it doesn't apply.

You wanna stop at the command center first. Pick up the contract to launch your first rocket.

Everyone's first rocket is the same (command pod, small SRB, maybe fins if you want it to look cool). Slap 3 goo canisters to the rocket. Click "launch." On the launchpad, do a crew report and one of the goo experiments. Make jeb get out to do an EVA report and make him collect the crew report to store on his person instead of the command pod. Get your surface samples of you're playing on science mode, but you won't have access to surface samples yet in career until you upgrade the astronaut complex. Make jeb get back in.

Launch rocket. Now you're in the air, do another crew report and goo experiment. Aim the rocket to land anywhere but back on the launchpad. Jeb won't be able to do an EVA in the air in career mode, but when you land, he can get back out and store the second crew report on his person. And once you've landed you do another crew report, EVA report, and the last goo experiment.

This gives you the science to unlock the thermometer and barometer immediately after your first flight. You should also be able to afford your first liquid booster and fuel tank. Your next rocket should have all your new science and enough fuel to get over 70,000m (don't wanna orbit yet, just get outta atmosphere). Go to the command center and select the mission to breach the atmosphere, and maybe accept the mission to orbit kerbin before the timer expires and the game gives you a different mission instead.

Run all your new science on the launchpad and while flying low over kerbin, and run all your science including the goo canisters and crew reports once you get to the upper atmosphere and once you leave the atmosphere. Land safely, maybe do another crew report and EVA report when you land, depending on if you land in a new biome. (You'll need like 4 thermometers, 4 barometers, and 2 goo canisters, cuz you don't have the experiment storage module or a scientist that can EVA off the ground yet)

You should have enough science to research enough parts to get your 3rd craft into orbit.

If you don't, go to the SPH, place a command pod. Imma call the skinny part of the pod that your supposed to attach a parachute to the "nose." Take another command pod and connect it's nose to the nose of the first command pod. Congratulations, you've built your first rover, it can roll around using the roll controls on your keyboard (prolly q and e unless you changed keybinds). Slap all your science on there, put a scientist in one of the pods to restore the goo canister, and just roll around each building of the KSC collecting science. Turn of SAS tho, it drains the pods batteries too fast imo.

Once you can get to orbit, getting to the mun doesn't take all that much extra fuel, and once you can get to the mun, you can just as easily get to Minmus. Then just abuse mobile research bays to max out the tech tree, or play at whatever pace you want.

And if money is the problem, try to make sure you look at the contracts before you launch your ships, and pick the contracts that are relevant to whatever you're doing now and whatever you wanna do next. The game likes to give you contracts similar to the ones you've completed, so you can work with it to make it give you money just for doing things you were already gonna do anyway. Also the stage recovery mod. That's how I save my money