What I really want to do is make my outlets always hot
Remove and replace the switched outlets. Don't
attach the switch legs (probably the red wires) to the new
outlets. Wire nut them together instead. Cap off the end one.
If you want to save one dollar
, install a jumper to replace the tab that had been taken out on the hot side of the outlet, between the screws.
To add your lights.... If you can get from one of the switched outlets, use the existing switch leg (and neutral/white) to feed your new recessed lights.
If you have to come from the switch, you are usually limited as to which switch you can come from. It must
have the switch leg and neutral in it's jbox.