Tutorial:Start a career game
Start-only tech, single mission
There are a number of ways to start advancing past Start. In fact, you can quickly leave its limitations behind.
For those who want to tie one hand behind their back to see how much they can do in one single mission with just the starting parts, here are two approaches.
The highest netting engine-less first mission involves stacking six (five gives nearly the same payout) Command Pod Mk1s in the Vehicle Assembly Building, turning the stack sideways with the A or D key, and rolling north off the LaunchPad across the Kerbal Space Center grounds to the Runway.
Start by taking and storing one Crew Report from the LaunchPad. Exit the pod to take the "EVA Report from LaunchPad", then take a Surface Sample, right click on a Command Pod to store data, then repeat with just the Surface Sample for each of the other pods. You'll repeat this procedure after rolling off the LaunchPad onto KSC and rolling up onto the Runway. It's possible to get a "Crew Report while flying over Kerbin's Shores" while in mid-air just after rolling off the north side of the LaunchPad.
Hanging on to a Command Pod for an EVA Report counts as "flying over Kerbin's Shores". However, in certain rare, poorly understood glitches (possibly related to split second timing while jumping on top of a ship), it is possible to get "flying over Kerbin's" EVA Reports for the LaunchPad, KSC, and the Runway.
Once on the KSC grounds, if your kerbonaut manages to be in ragdoll mode (not standing up) while on the ground, you can take an EVA Report and Surface Samples from the Shores biome. Repeat the Surface Samples four more times.
Rocket Surgery to Minmus
Probably the highest earning single Start mission using all the parts employs an elaborate form of explosive decoupling that KSP YouTuber Scott Manley dubs "rocket surgery". In his video "Kerbal Space Program - 0.22! Lets Do Science! Lots Of Science", he uses solid rocket boosters to push a primitive lander rocket on a mission all the way to Minmus and back. The mission depicted netted 351.5 Science.
It's possible this tech could also reach Duna.