horizontal .vs. diagonal .vs. toeclips+straps

Don't ride fixed when you have knee problems already- it'll only get worse.

Not necessarily true.

Don't push weights or gears that are too big, pain and damage will also depend on the nature of your knee problems.

Indra is right here, I (used to) have minor knee problems and soreness but then geared down to a lighter ratio and the pain in my knee was more or less gone.

-Back to topic:

I ride with toeclips + double straps, and I have never tried any different ones because I like to ride without changing shoes when I'm not cycling. Clips and straps aren't too bad tbh, they do fuck up your shoes so make sure if you are choosing clips, wear shoes you don't really care too much about. The only other problem with toe clips and straps is that the straps could possibly tear but this has never happened to me after about 6 months of me using the same straps and my brother using them for a year.