In my job of fitness we have a saying, the goal is to keep the goal, the goal. When pursuing a goal, it's easy to get distracted by a bunch of other stuff. Focus.
What is the goal of this game? To put a person on the Moon and return them safely to Earth - before anyone else does! So you do the absolute minimum of missions you can to achieve that.
Before you can do manned lunar missions, you have to do at least the lunar flyby probe mission. Before you can do that, you have to do the orbital satellite. From there, technically you can just open Gemini/Soyuz Lunar Landing, however it'll take forever to get the reliability up and if your first manned mission in space is to the Moon the reliability penalties will get everyone killed. So in practice you need the one-man capsule in Earth orbit, then the two-man capsule, and from there either Gemini/Soyuz Lunar Missions in Earth Orbit. Apollo takes extra time, and the UR-700/UK-700 approach is one you can only do if you have stacks of spare cash and/or lots of time.
Below is the shortest approach I've found. Only after the first successful mission of one do I open the next programme. This ensures the best reliability carryover, eg opening Mercury and Gemini at the same time is not as good as getting Mercury's reliability up to 80+%, doing an unmanned suborbital, and THEN opening Gemini. I list the minimum missions, anything after that (like manned duration missions) are just a bonus if you have spare time or want a prestige boost, and are not necessary to the ultimate goal.
1. Orbital satellite + suitable rocket - minimum, orbital satellite mission
2. Lunar flyby + suitable rocket - only one mission
3. Mercury/Vostok + human-rated rocket - earth orbit - first unmanned suborbital, then unmanned orbital, then manned orbital
4. Gemini/Voshkod + human-rated rocket - earth orbit - unmanned suborbital, unmanned orbital, manned orbital, eva and docking
5. Gemini/Soyuz Lunar Missions in Earth orbit + human-rated rocket (you can use the same as before, but this is a good time to start working on the Saturn V or N1 that can get you to the Moon) - unmanned suborbital, unmanned orbital (of both capsule and lunar landers), manned orbital, docking, eva (remember this will be a different spacesuit to that in the previous step, so you have to get the reliability up)
6. Gemini/Soyuz Lunar Landing - unmanned lunar pass, unmanned lunar orbital, manned lunar pass, manned lunar orbital, then...