Congratulations on your decision, I have a Vita and it's awesome piece of hardware with a lot of unforgettable software, owning one makes me feel like owning a Dreamcast back in the day, so many jewels I could have "lost" if not buying it...

About your questions:
1- Is the 8GB memory card enough for it?
I have 16GB and think is too small, and it gets me angry to have to delete some games I have to download anothers... If you have PS Plus, there will be monthly digital games for you to download for free, and your Memory Card will be soon full... Also there are amazing PS1 and PSP games to download I would recommend you Tomba!, Tekken 2 and 3, there are also amazing JRPGs and many other games on the PS1, on the PSP I can recommend Ape Escape On The Loose, Megaman Maverick Hunter X, and there's a lot of other stuff i don't recall now! Digital only games for Vita like Escape Plan (puzzle)

2- Is the Borderlands 2 port really as bad as people say it is?
Didn't play it. But mostly people compare the game to PS3 so they will say it's TERRIBLE when it's just a little downpowered.

3 - Is the PSVita fragile enough where a case is required or strongly recommended?
At least a case for you to store it

4 - Are there any peripherals or accessories that are strongly recommended for it?
I would recommend buying an extra charger, I do also have a battery expanser (forgot the real name of this things)

5- Is the Vita region locked?
Your vita will be compatible with every physical game, from wherever, but for digital downloads or DLCs it needs to be from only one country's PSN, if you buy a Japanese game you won't be able to download it's DLCs.

6 - Lastly, recommend me some games.
Depends on your genres preferences, the Best vita retail games in my opnion are:
1 - Gravity Rush (you can turn off the "gyroscope" it will make gameplay 10x better)
2 - Tearaway
3 - Persona 4 Golden
4 - Killzone Mercenary
5 - LittleBigPlanet Vita (I think Europe has a version with DLC included, but not sure)
6 - Sly Cooper Thieves In Time
7 - Uncharted Golden Abyss
8 - Muramasa Rebirth
9 - Final Fantasy X|X-2 (X-2 will be digital only)
10 - Soul Sacrifice / Delta (Delta is digital only)
11 - Freedom Wars
12 - wipEout 2048
13 - Tales of Hearts R
14 - PlayStation All-Stars Battle Royale
15 - Dragon's Crown
16 - Oreshika (digital only)
17 - Dokuro
18 - Sly Collection (PS2 Remasters)
19 - Ratchet & Clank Collection (PS2 Remasters)
20 - God of War Collection (PS2 Remasters)
21 - Jak & Daxter Collection (PS2 Remasters)

The Neptunia series confuses me but Re;Birth 1 is $6 on PSN right now.  Is it a good entry point?  Or do I need to play the older games first?

That is the "oldest" game. Or more accurately, a remake of the oldest game. Best place to start and a bargain price

What Roronaa_chan said. These games are remakes of the first three games from the PS3, and they are stellar as Vita games. It helps that they took the PS3 games, changed what people hated about them, and gave the Vita improved experiences all around. At $6 for Re;Birth 1 right now, you can't really go wrong.

8GB isn't enough space and it's not fragile either, I dropped it a few times and there is no damage to it, it's build quality is great.

I have 8 GB memory cards and its enough for me. You can transfer your games (digital, save data, etc) to your PC as a storage and delete them in your Vita once the transfer is completed. That is what I did because I don't have enough money to buy larger memory cards and most of the money I spend on buying games. Its quite pain because you can't cut and paste into the PC but no biggie.

As for Borderlands 2, the game is great on Vita and played smoothly after the patch. You just need to download the update (it'll come out automatically after installed) and you are good to go.

Most of your questions have been answered from the above posts so I'm gonna leave it there

Borderlands 2 will actually take up about half of the space on your card (the bundle has the digital version) so no, it probably won't be enough space, especially if you ever get ps+.

Also, borderlands 2 on the vita is really bad. I was excited to play it on a portable system as I loved the game... But it is pretty much unplayable on the vita. You have to map some buttons to rear panel which is awful. Frame rate dips to horrible levels, and obviously the graphics took a major plunge (but that isn't that big of a deal).

Personally, my favorite games for the system are persona 4 golden and the daganronpa games. Suikoden 1 and 2 on the ps1 are must buys as well if you haven't played them.  Uncharted isn't too shabby either. Also, Make sure you research these games that people recommend to you here. I have found the vita fan base has some different tastes in general and I have to be careful when I pick up recommended games...

8GB definitely isn't worth it. 64GB all the way.

Borderlands 2 is alright. Depends on your perspective. If you hold it to the standard of other handheld games, it's actually a really impressive feat. If you hold it to the standard of home console games, it's easily the worst version.

Vita isn't fragile, but I'd strongly recommend getting a case anyway.

And ABSOLUTELY buy a screen protector. Cannot stress that enough.

Vita isn't region locked. I've never imported so many games as I have with Vita. You'll want to bookmark Play-Asia and Videogameplus ;)

Recommendations? Based on what you already said, you seem to like Japanese stuff - so DanganRonpa 1 & 2; Atelier Totori Plus; Ys Memories of Celceta; Tales of Hearts R; Oreshika Tainted Bloodlines; Shinobido 2 and Demon Gaze would be among my recommendations.

Thanks to everyone that responded, but I have one more question. So, I'm most likely going for the 32 GB memory card, but if I buy a game, then delete it to save space, can i redownload the game I deleted for free or is it gone forever?

8gb is good enough if you plan on only buying physical, problem with that is that there's a ton of amazing games that are only digital