Shoot the Bullet, while fun, was technically slapped together by ZUN to go along with something else I forget for an event. Where as Double Spoiler had more time and development put into it. I actually enjoyed both.
As for where to start, all up to you. If you want you can just start off with the PC-98 era games and go from there. I'd recommend T98-Next as the best PC-98 emulator for the PC-98 Touhou games. Does not necessarily require an incredibly powerful PC to run it but it helps.
As for the Windows games, any decent two to three year old PC ought to suffice, even as far back as six years should be fine to run all the games; so long as you have a decent graphics card as well. I say start with "
" only because it's the only one of the windows game where you don't have an indicator of where your hitbox is. In the later games when you use focus shots you'll see a small white orb indicating your hit box, starting at "Perfect Cherry Blossom". By then though you'll have a greater grasp at how the game play is.There's in fact a fan-made EoSD graphics update that alters the boss sprites and some of the enemies as well to match up the graphics of the later games such as Subterranean Animism. It even throws in the option for you to put in a hit-box indicator if you want. I personally wouldn't use the hit box indicator
Oh yeah I almost forgot, in regards to the windows era touhou games,
DO NOT LET THIS HAPPEN TO YOU AS IT MAY CAUSE INCREDIBLE RAGE
This kind of mistake seems prevalent enough that there's a doujin manga that comments on this kind of mistake