Welcome to the Verse! I can't give you much advice regarding how to secure your sticks considering that I've been flying with unmounted sticks in SC for over a decade now. That said, I can tell you that playing AC repetitively will burn out your hands and wrists much quicker than in the Persistent Universe (PU) given the much more repetitive nature of the AC maps. If you are like me then you will likely spend a lot more time in the PU doing other things than ship combat, like simply traveling between POIs as well as FPS combat, mining, salvaging, looting, etc. I do ship combat to be sure, but when it's interspersed with other things then I find it less taxing on my hands and wrists.
I'd also encourage you to go ahead and jump into the PU and not worry too much about losing resources as this is still very much an Alpha game and it's very likely that your character will be reset in the PU with the next major update anyway. You can always buddy up with someone experienced in the PU by asking in chat or utilize the Guide System to locate one of the many, helpful volunteer guides. I would also recommend doing the tutorial if you haven't already, but if you didn't do it initially I don't think it will give you the option again until after the next wipe.
The only tips I can give regarding combat is first to practice and second to make sure you are never flying in a straight line while in combat. Combat has changed in 3.23 with the introduction of Master Modes, so many of the resources I might suggested for reading/viewing are a bit out of date. Still, you might want to check out the Legacy Instructional Series. Again, some of the information is a bit dated in regards to the mechanics of things, but the core concepts they put forth for combat training still largely hold. There are also a number of resources listed on the official "Learn How to Play"(https://robertsspaceindustries.com/playstarcitizen) page on the RSI website, which you might want to check out.
As for requesting a hangar, that can be done either using the comm's MFD in your ship, the comms app in your Mobi (port ATC is listed under Friends), or by mapping the request landing keybind (it may be already bound to hold N, but I can't say for sure right now as I have a custom mapping for that action [backslash]). The mapping can be found in the Options menu by clicking "KEYBINDINGS" -> "ADVANCED CONTROLS CUSTOMIZATIONS" -> "Flight Movements" -> "Request Landing".
Again, welcome to the verse and I sincerely hope you enjoy your experience.