I am looking to buy a used S4 for Verizon to keep my Unlimited plan. I read somewhere and someone mentioned 2 different software's; MDK or ME7. Are one of these root? Should I avoid one of these?
I don't want a rooted device, just an S4 in great shape and a clean ESN for a fair price.
That's the software version (or the last 3 characters of the "baseband version" on the Phone information screen). The phone was released with MDK, then was upgraded to ME7, and just a few days ago the MI1 update was released.
By itself, none of these versions indicate that a phone is rooted or not, it's just that if you want to root *AND* install a custom recovery, the phone must be on the first version of software, MDK...that's why it is so often mentioned. I imagine pretty much any non-rooted phone out there has, at this time, been updated to at least ME7, unless it's a device that was purchased a while ago and hasn't been connected to the network.
To simply answer your question though, no, there is no reason to avoid a phone based on it's current baseband version, especially if you don't care about root. There are other things you may want to look for (like a clean ESN as you mention), but the software version
by itself shouldn't be a red flag for anything.
EDIT: Based on the OP's question, I'm obviously assuming he's referring to the Verizon version of the S4.