Good God. The "Tiny little screen" will not effect your eye sight unless you strap it to your forehead and stare at it for 10 hours. Like VR, 3D, LCD, Plasma, Tube Tv's it is advised to take a break every 30 mins or so to rest the eyes and brain.
As for remote play it's ok, not great as you are forced to play at a lower resolution than the ps4. Also the games can chop up at times. The Vita comes into its own when used without a ps4, you basically have a portable ps3. AAA software is limited but the Vita beats all other handhelds to a pulp, including the switch (imo).
I bought my Vita 2 years ago for 80. I suggest you look around for deals otherwise you will end up paying 200+.