Yes, that would be OK for plants. The bulb combo you list is very good for plants. If you go with the less expensive brands like Zoo Med or other import brands you more than likely get mediocre reflectors. The higher end fixtures like Coralife or Aquatic Life give you high efficient reflectors that maximize the light produced. Also they use higher quality ballasts and extra features like independent timer control. On your 22" tank a Zoo Med would give you medium light while the higher ends would give you med-high light.
If you're like me budget decides. I call my tanks "Watery Money Pits". OS.