There is a lot of variation in where people end up living. There's a pretty good mix of east and west, but the west side has been typically the choice of a lot of students because that's where the 'fun' is (alamo draft house, bars on cinncinati street, trendy restaurants and cafes). MS1's with families normally end up renting houses on the west side, but there have been some instances of MS1's finding people to room with and rent a house on the FB page, and sometimes it ends up cheaper than an apartment. Of course, many people get apartments, and a lot found roommates on the FB page. There are plenty of apartments within 15 minutes of school, I would suggest looking around the Sunland park region, and the area near the Alamo draft house. Some complexes I've like are Avalon West and Legends. As for the east side, it's growing, and there are new complexes out there. Plus the traffic going to school is non-existent coming from the east side, but you do sacrifice being close to classmates and all the stuff to do on the west side. My advice is to find a place 15 minutes from school on the west side of town, in my opinion, it makes for a better experience.
Regarding roommates, you can post on the FB page if you are open to having a roommate, but if you want to live alone, the housing prices in El Paso are pretty reasonable, so you won't be breaking the bank too much if you don't want to live with anyone else.