Strange... ...Hard to imagine why anyone would move into the "loop". Particularly someone on a budget. Do you rent or own? I couldn't figure it out and got very confused by the mention of apartments that didn't come with appliances. In my thirteen years of living in Chicago proper I have not heard of such a thing. Its a big city with lots of affordable housing, complete with appliances.
Perhaps it is your choice of neighborhood. The loop is primarily a business district. Great for the swanky and well-to-do but since you are new in town and claim to be on a budget you should consider hopping on a bus or the 'L' and heading into other neighborhoods. To start, you might like Wicker Park. Just take the BLUE line to the Damen stop- Then wander around. Lots of small shops, books stores, cafes, bars, etc. For your next excursion head to Lake View. Just take the RED line to the Belmont stop- Then wander around. Similar stuff but different then what you will find in Wicker park. Consider these your starter neighborhoods.
Beyond that I recommend doing your homework and/or joining some local interest groups:
CTA (Chicago Transit Authority)
http://www.transitchicago.com/
Neighborhoods of Chicago
http://en.wikipedia.org/wiki/Neighborhoods_of_Chicago
MeetUp
http://www.meetup.com/
Yelp
http://www.yelp.com/chicago
You've mentioned you are new in "town" and looking for things to do and people to socialize with but I didn't read anything in this thread that describes what interests you. Beyond Mobile Reading that is.
As for me, I'm a Chicago resident. I live in a neighborhood known as East Rogers Park which is way up north but very affordable and also in spite of gentrification still quite culturally diverse. For work I head down to Streeterville which is the area east of Michigan avenue and north of the Chicago river, near the apparently rather famous West Egg Cafe.
Anyhow, hope this helps. Do to being a creature of habit I'm not a Chicago expert by any means but I figured this little bit of advice and information would be better then nothing.
Feel free to inquire about anything more specific then the city as a whole.