Vertical:
For 600pts you can try Soldier Blade which NL gave a 9/10 or
For 900pts you can try Star Parodier which NL gave a 9/10 or
For 800pts you can try Musha which NL gave a 9/10 or
For 600pts you can try Blazing Lazers (Gunhed in Japan) which NL gave an 8/10 or
For 700pts you can try Final Soldier which NL gave an 8/10 or
For 700pts you can try Detana!! Twinbee which NL gave an 8/10 or
For 600pts you can try Super Star Soldier which NL gave a 7/10 or
For 800pts you can try Star Soldier R which NL gave a 7/10 or
For 500pts you can try Galaga which NL gave a 7/10 or
For 600pts you can try Galaga 90 which NL gave a 7/10 or
For 500pts you can try Zanac which NL gave a 7/10 or
For 600pts you can try Dragon Spirit which NL gave a 6/10 or
For 600pts you can try Gaplus which NL gave a 5/10 or
For 500pts you can try Star Soldier which NL gave a 5/10 or
For 500pts you can try Xevious which NL gave a 4/10 or
For 500pts you can try Star Force which NL gave a 4/10 or
For 500pts you can try King's Knight which NL gave a 3/10

I highly recommend Star Parodier, but be warned it is CUTE! I also love Xevious (eventhough it has a super bad score from NL) but my love is based soley on my nostalgia of nights wondering a bowling alley while my parents played in their leagues and I played the half dozen arcade machines to death. Xevious being my favorite. Other than that, check out the NL reviews of the above mentioned games... they usually do a fantastic job of telling you the difficulty level.

^ Thanks for you recommendations, manleycartoonist. But are you sure that the games you listed are NOT hard? I'm especially searching for some easier Shoot em ups. I tried Dragon Spirit (which is also in your list) and I think it is extremely hard. I can barely make it to Stage 4 (of 8). Can you recommend some games that are easy enough for average players to play through? (Or doesn't such games exist in the Shoot'em up genre?)

Star Parodier, Lord of Thunder, Gley Lancer, and Soldier Blade are the games you're looking for. They're are actually fairly easy, and 3 of them has set-able difficulties in case you're still having trouble. Still, it should be noted that Shooters are games of skill. You should expect to die a lot until you learn the ropes.

Part of the fun of Schmups is the frustration from losing so many lives. The fun of getting into the Zone and dodging bullets that seem impossible to dodge. For some reason I actually like Shooters that don't have shields... one shot one kill has a certain thrill that is missing in most genres.

If it's an easy shooter you're looking for, then Star Parodier is what you want.

@Omega - like cheetah says, Star Parodier is an excellent choice. You can change the difficulty settings if you want (there are three).

@MickeyMac, @Cheetahman91, @StarBoy91: Thank you. Star Parodier seems to be what I want because all of you said that. And sooner or later I try the other games that MickeyMac listed, too.
@manleycartoonist: Yes, I know that some people love the extreme challenge and being tortured. But no. I don't. I'm really searching for shmups that are "beginner-friendly".

BTW: I loved R-Type DX on the Gameboy Color and Gradius Advance (AKA Gradius Galaxies) on the GBA and Parodius on the old black & white Gameboy. They were pretty challenging sometimes but I had no problems to completely play through.

@Omega

If you like R-Type, make sure to give both the original, and Super R-Type a look(Super is easier and has adjustable difficulties). And you might want to try the original Gradius for the NES, too (NES version is easier than the Arcade version thanks to slowdown). Just thought I'd throw that out there.

Oh, and Axelay! I forgot that that game is fairly forgiving.

CONSIDERING
Donkey Kong Jr.
Donkey Kong 3
Yoshi
Yoshi's Cookie

DK Jr. and DK3 are both great arcade games, and the two Yoshi games are decent, though not amazing, puzzlers. Not bad choices, though the DK games should definitely get priority.

If I were you, I'd CONSIDER saving my money. None of those games are any good. Donkey Kong Jr. Math is one of the most boring games I've ever played, Donkey Kong 3 is...okay, I guess, but you can do far, far better on the VC. Yoshi is just pure drivel and Yoshi's Cookie is easily one of the worst Block-Puzzler games on VC.

@mickeymac: I am not getting DJ Jr. Math, if you didn't notice.

Donkey Kong Jr. actually looks like fun. It appears to have the same appeal as the first game.
Donkey Kong 3 is a bit weird, but it looks like it takes some inspiration from Space Invaders.
Yoshi and Yoshi's Cookie look like fun puzzlers. Yoshi's Cookie looks challenging. I love puzzle games.

Got some Wii points left and was thinking of getting either Mario Kart 64 or Super Mario Kart.
What are your pros and cons of each game??

Well if you have Mario kart wii or plan to get it I would get super Mario kart its different than the other ones. If you don't plan to get the wii version I would get super Mario 64 because they are almost the same except wii version is better.

Get SMK, it's a classic. MK64 hasn't aged well.

I'm trying to decide what to get with my next points purchase. I'll have 1000 points leftover after I get Cave Story. Should I get:

Bit.Trip Core
Bit.Trip Void
Ogre Battle: March of the Black Queen
Ogre Battle 64: Person of Lordly Caliber
Contra ReBirth
Blaster Master: Overdrive
Ironclad

Is indiana Jones any good?

Did you like Bit.Trip Beat? if so get the sequels first. I also really liked Blaster Master: Overdrive.

OK, here's my plan for the summer.

NES
Wario's Woods
Yoshi
Yoshi's Cookie
Kirby's Adventure
Donkey Kong 3
Donkey Kong Jr.
Zelda II

SMS
Sonic
Sonic 2

SNES
Super ROTJ
Indiana Jones

GENESIS
Sonic 2
Sonic 3
Sonic & Knuckles
Columns

I should've known better than to be lazy...

Bit.Trip Core/Bit.Trip Void - I played the first and enjoyed it immensely, and I'd to try the sequels

Ogre Battle: March of the Black Queen - I already gave it a go not to long ago and loved it, and I've recently had the urge to give it another go, this time legally.

Ogre Battle 64: Person of Lordly Caliber - It's the last N64 game I need to get on VC, and I've also heard it improves on its predecessor, though some still say the first was better.

Contra ReBirth - I watched a stream of the first few levels, and it looked really good. I love Contra, despite the fact that I suck at it, and this one seems easy enough that I might actually be able to make progress in it.

Blaster Master: Overdrive - I greatly enjoyed the first, though I'm still working my way through that game, and from what I've seen, this one isn't as good as the original.

Ironclad - I love shmups, I love the Neo Geo, and I love the style of this game. It also seems to contain elements from my favorites in the genre.