I am taking an arsenal of supplements to see if they help ameliorate a health condition. Plenty of pub med articles elucidate the benefits of curcumin (turmeric), Co Q 10 and krill oil, and keeping omega 6 very low. Then, less information but still potentially helpful : MSM, lots of green veggies, avoiding dairy and certainly processed foods, etc. I think the higher DHA fish oils and krill oil will give you more bang for your buck than your run of the mill fish oil. I just eliminated dairy to see if this helps.
You're correct that you'll find plenty of conflicting information on acid-alkaline balance online, so I'm not sure how to help you there, except that there is more agreement on the above information. Lemon and other low sugar fruits are supposedly preferred, and of course avoiding sugar and all substitutes, moderating alcohol and conventional meat consumption, probably.
This guy seems to have his head on straight, too: Cooling Inflammation