Some games work really well, especially games that can remap controls. You can't remap the controls in the PS4 settings, but if you can do it in-game it'll work. I enjoy it.
There have been a few times where it drove me nuts. Playing Uncharted 4 I had to swap L1 and R1 for shooting just because I couldn't map L1 to aim, instead it had to be fire.
Prey has been the same way. I have to use the touch pad on the back to attack. Otherwise it has been fine.
I played Persona 5 with it and it was great. Especially if you have to sit and watch a show with the kid or your wife wants to use the TV.
One thing to note is if you have multiple PS4's in the house. The Vita can take one sign in to PSN and that has to be the account you use on your PS4. If you change your PS4 log in with all your saves you'll have to reset your Vita. Well, you get 1 reset on your Vita for so many months. I haven't done this, but I read about it and voted against it. It even has a warning when you want to reset your Vita to change your PSN credentials.
I'd say you'll really enjoy it when it works. The touch pads on the back are my only downside. Some games make it work while others it's just hard to get to use to. There are some unofficial add-ons that help, but I only have the trigger case for R1/L1.
What helps me is that I have a ton of PSP, Vita, and PSN downloads. I get a lot out of it. I dislike not having a lot of space on my micro SD card. I own two of them, but they aren't big and one I keep in my PS TV.
I'd say you'll like it, but I'll just warn you about the triggers. You might want the add-on just in case (I don't even know if they work that great). Unless I'm hearing other people talk about it and I haven't researched it.
If you're really looking for a work around a busy schedule then go ahead and get one. I really enjoy my Vita.
Note: plug your PS4 into the router and don't go wifi with your console during remote play.
You could always play on your PC and I saw this video the other day where someone ran a screenshare program from their PC to their smart phone and played that way. TeamView, so there might be other ways to play. The internet connection has to be good though. I have cable and I have it plugged in from the router and it works for me.