BG66 is quite ok for net play..normally ppl would have more tension for better controlling
but remember, higher tension might not generate enough power for your clears
for starters, maybe you can try increasing tension to 24lbs..MIGHT have better results
but if you think 22lbs is already good enough for you, then stay with it

BG68ti or BG85 are also good choices i guess

For control and net play, thicker string or higher tension might help.
The classical BG65 is good and cheap for control.
BG80 also not bad, although it is also very good for attacking.

Just my personal opinion. Hope it helps

for attack play, choose those with head heavy rackets
for that budget, you can consider victor and some of the yonex-es