It sounds like you're being somewhat influenced by the minmaxing/power gaming mentality of many Shadowrun players. I think a big reason they do this is because the priority system practically encourages it, going for thematic elements often means you're dumping karma down the drain. I like to stay true to my character at all costs, and I see you do as well. So I know the pain you're experiencing here. One thing I'll say is that there are no required skills, not exactly. It is perfectly fine to start the game with Spellcasting 4 instead of 6. You don't absolutely need to have Conjuring. People say that mages should always have ranks in Pistols but that isn't actually true, it is quite likely that you won't even need that pistol and if you get caught in a bad situation where a pistol would save your ass, oh well, your character just doesn't know how to use pistols and you suffer the consequences. But what about all those other situations where that extra karma you saved on pistols got pumped into your foci? It's all about tradeoffs. Then there are SIN's, people say you always need 2 to 4 or more at max rating to start the game. That is false. People are afraid to have their character get into bad situations so they try to create what they think the perfect runner is, but the truth is that there is no perfect runner.
It seems like you think that you need to purchase spell formulas during character creation, as far as I know, you don't. They are included as part of the priority system. Speaking of that, have you tried Point Buy? That's my preferred method and it is imo the best system for people that like to have very well fleshed out and realistic characters, not just combat monsters with perception and sneaking, I see that alll the time, those are cardboard characters made by people that want to do maximum damage.
It seems to me that you want to have priority E allocated to resources but can't find a comfortable way to manage it because there are so many things you feel are important. Shadowrunners that actually have next to nothing for gear are probably in a tight spot for some reason or another. Perhaps they were robbed, perhaps they had to pay everything they had and sell most of their gear to pay a gambling debt. Maybe you had a Force 8 Weapon Focus but you don't any more. Maybe you used to be a hot shut runner riding a Eurocar Westwind 3000 but you got fucked over somehow. There has to be a reason you have badass attributes and skills pertaining to shadowrunning but you don't actually have much gear. I think you should play with priority E for resources like you planned but start out in very rough shape. I'm talking about no SIN, no vehicle, no foci. You have your lodge and some necessities, perhaps a few toys you managed to hold onto. You are basically starting from scratch. Will it suck without a fake SIN? Probably, but you might be able to get one quickly. If not, oh well, shit happens. You suffer it out, it is a game after all. I think it will all work out for you in the end and you'll be glad you did it. And I would take power gaming advice with a grain of salt, it doesn't really matter because a good GM is going to put you against appropriate challenges anyway. The guy with 20 attack dice and nothing else on his character sheet is going to have fun killing but that's basically all he can do, don't take advice from those types of players.
And yeah, everyone should play their way and have fun. If they like that kind of character and have a good time, great, but I can tell that you want something a little more realistic.