Which wine kit specifically are we talking about? Could make a difference.
I'd say 68 is a tad on the cool side, but you should be ok. Might have a little lag time when the wine needs to clear out, but fermentation should work. If you have any issues at the end, I'd advise a brew belt, but at 68* it is worthwhile waiting to see what happens first.
You don't have to take readings daily. Depending on the kit, you probably do not have to stir daily either.
Assuming we are dealing with a fairly standard kit, you are probably fine waiting one week, then rack, then wait one or two weeks, then taking a couple readings to make sure it is finished.