I am currently look for a guitar for 700$ or under.

I mostly play things from alternative rock to classic rock leads to heavier stuff like metallica. I am currently interested in the ESP LTD MH-350NT STBLK, it has an EMG 81 & 85 in its bridge and neck positions, I will most likely go with this guitar, so if any one has played it let me know if its worth the money! I dont need any kind of tremelo, I prefer ESP guitars, but I may be willing to go for something else. I really like the EMG 81 & 85 setup, and preferably 24 frets. I use a Peavey Vypyr amp, so if you guys know anything thats sounds amazing through that, go ahead and let me know!

I just need general suggestions that meet most of these criteria, it doesnt have to follow all the criteria, but needs to be along those lines, and of course, have heavier tones.

Thanks to all who suggest,

I've played one in a brown burst. It was used but it was actually pretty incredible. It WAS unplugged at the time but it felt pretty tight. Whoever owned it before had it drop tuned and some heavier strings though. So that may have affected my love for it. lol. Also. One of the deepest belly cuts I've ever seen.
If you bought it new at full price would it have been worth it? Whats the quality?
At $700 there may be better, but this one is pretty great. Quality felt good from what I felt for the few minutes playing it. Whoever owned it before did a bad setup of the pickups though.
Go used for that price and you can get a nice MH-1000 or or H-1000 with your specs, but they might have a trem. I've played most of the ESP line and would only play an LTD 400 series or better. The 1000 series however has a better built quality now a days especially since the 400 series is no longer made in Korea. Here's some guitars I found for you but you can keep digging and find more.
ESP E-II Horizon FR
Gibson Flying V HET SET
ESP Eclipse II FM JB/Jazz
EBMM Majesty
Marshall JCM2000 DSL/ JCM800 1960a cab
Mesa Mark V 25
I have outed myself as an EMG hater, but I would actually be careful about those pickups. They're great for tight high-gain sound a la Metallica, but I'm not sure they work too well for rock/hardrock sounds, even less for clean.

You may be perfectly satisfied with them, it's a matter of taste mostly. One alternative I think is worth trying is a Jackson DK2HT or DK2MHT (M means maple fretboard), that comes with Duncans. They don't give you quite that Metallica sound, but are more versatile imo. Not saying that the LTD you're looking for is bad, just suggesting an alternative that may be worth trying.
I used to have a MH350-NT, same color too, a couple of years back, and wasn't overly impressed with it. The placement of the bridge volume knob was what really drove me to stop playing it and eventually traded it in. It's placed in an awkward spot where my pick hand pinky would keep brushing it and turning it down (and it spun really easily...), especially when palm muting arpeggio-ed notes on the g, b, and e strings. Try it first yourself to see how it feels for you and your style. Another strange thing I noticed was even though it was a newly made guitar, it still was all soldered inside (the pots/battery etc) instead of using the EMG quick connect system (but the pickups themselves were quick connect).
ESP LTD James Hetfield Signature Vulture-Satin Black
ESP LTD James Hetfield Signature Snakebyte-Snow White
ESP LTD James Hetfield Signature Iron Cross-Snow White
Jackson Pro Series Soloist SL2Q Trans Root Beer Quilt
Jackson SLATXMQ Soloist3-6-Trans Red Quilt
Jackson Pro Series Dinky DK2QM-Chlorine Burst
Jackson Pro Series Monarkh SC-Trans Purple Quilt
Schecter Hellrasier Hybrid C-1 Ultraviolet
Ibanez Iron Label ARZIR20
Schecter Hellraiser C-1-Black Cherry Burst
Ibanez RG-770-Laser Blue
Jackson Kelly-Trans Green Flame
Line 6 Helix LT