I would buy it in a heartbeat thanks to the 3rd party support that they've given the previous two. The Vita is my most played console this Gen for a reason.

I own a vita and I don't understand the "Vita has no games" saying. I don't know if it is because I am a RPG fan at first but I have enjoyed a lot of game on the Vita, from the PSP library to games available for the Vita.
So if the next handled support PSP, Vita library, I will get one.

Maybe. Vita supported a bunch of great games this gen but few of them are exclusive. The problem with a theoretical PS handheld is that Sony's first party content isn't very good and third party games would probably be multiplatform. I look back on the Vita and see one truly great first-party game, Wipeout 2048, by a studio closed shortly thereafter. And many of the great third-party games - Guacamelee, Retro City Rampage, Severed, Virtue's Last Reward, etc. - are or will be available elsewhere.

If this handheld could secure better first-party games and some exclusive third-party content I would definitely consider it.

Nope (and I have a Vita).

Sony aren't in a position to support it (their best devs don't like portable) and japanese devs will favour Nintendo.

I already loved PSP and PS Vita and if the rumors are true and the new handheld can play PS4 games too then... HELL YES!!!

Probably, Would need to know what it was all about first.

I would definitely buy one, but not at launch definitely. Luckily for me the vita is home to niche japanese 3rd party games as well as jrpgs.

Of course. Best handheld ever created was by Sony.

a new portable handheld with PS/PS2/PS3/PSP&Vita BC from PS store and maximum price of around $300...

Yes

Most likely not. My Vita basically collects dust. It would take a bunch of great exclusives to change my mind.