Borrott, welcome to the forum!

W/ re: will adding bleach effect pH - according to chem_geek the high pH of the bleach is negated by the acidic reaction of 'zapping' the 'nasties' in the water so the net effect on pH = ~ 0. With that said, I'd change whichever parameter needs the most 'tweeking' first (if the cl is way low, do that first - if the pH is low and the cl ~ok, bump the pH first). If you do as CarlD says and "keep ahead of your water..." this will probably not be an issue most of the year, though for start-up things may be a little more demanding (in terms of time spent and attention/ dosing).

You are doing the BEST!! thing for your pool by comming here and asking any questions you have!

Happy swimming! - Waste