There's really no right or wrong order to play the games in, most folks just start with the Windows games and go from there. Couple points to bring up:
- The jump from extra to hard is much more manageable than the jump from hard to lunatic. If you're struggling with lunatic mode, consider turning the dial back to hard mode and using that as a bridge.
- The PC-98 games, from what I've found, are actually easier than most the Windows games. They're a little more simplistic because of their age, but Touhou 2 (Story of Eastern Wonderland) and 4 (Lotus Land Story) take the cake as the easiest games in the series. I personally use Anex86 to emulate the PC-98 hardware as Neko Project was giving me wicked slowdown.
- Phantasmagoria of Flower View (Touhou 9) and Phantasmagoria of Dim. Dream (Touhou 3) have pretty complex mechanics since they're head-to-head games, so I'd personally recommend watching a tutorial video that explains all the systems. I'd also recommend starting with Dim. Dream first, as there's nowhere near as many bullet and I find Yumemi to be an easier final boss than Eiki Shiki.
- If you haven't already, download the thprac software. It lets you jump to specific parts of stages and boss fights, which is good for practicing sections that give you lots of trouble. There's nothing wrong with going on YouTube and looking at other folks' gameplay too, some of the spell cards can have cryptic dodging strategies and still require actual skill to pull off.
- Pointdevice mode only appears in Legacy of Lunatic Kingdom because the game was designed around being crazy difficult. There is a legacy mode that reverts the gameplay back to a standard Touhou experience, but I'd still recommend clearing pointdevice first for the practice.
As I said before, the best order to playing the games is the order you choose. I personally started with 6-10, then backtracked to 1-5 to clear the PC-98 catalog (currently finishing up 4).