A nice desk for 80-100$?

depends on your definition of good. would it work? likely. its cheap foreign made flakeboard throwaway furniture though.

generally for under $100 your options are limited to generic cheap throwaway furniture you can get at walmart, ikea, etc. it will work, however i would not consider any of it high quality nor good - adequate at best.

the metal ones such as http://www.walmart.com/ip/Santorini-L-Shaped-Computer-Desk/12528411 are a little more sturdy than flakeboard however you still get what you pay for and while a bit longer lasting than flakeboard are still not great. at minimum i'd look for something which has a metal frame - those flakeboard only models are held together with only a prayer (little clips and slots generally)

if you, your family or friends have tools or know how to work with wood you can build a much more solid desk from lumber yourself using actual plywood or solid wood depending on what is available to you.
 
what kind of desk would you build? that depends on if it needs to be freestanding, if its in a corner or if its in a cubbyhole.

there are lots of plans available free online for wood computer desks you could look at for ideas https://www.google.com/search?q=computer+desk+wood+plans&es_sm=122&source=lnms&tbm=isch&sa=X&ved=0CAgQ_AUoAmoVChMIjue9hLWSyQIVxkUmCh3arQZL&biw=1366&bih=643

if its a corner desk and you can screw into walls (permanent desk) running boards along the back 2 sides for support and just having 2 legs on the corners makes for a strong desk with minimal material. if its a full cubbyhole area, 3 sides with boards on the walls makes a very strong desk without legs. for freestanding you have your choice of either using a 4 leg design or with plywood sides (you can see plans for ideas)

if you do not have tools or the skills to build furniture just buy one and realize its inferior quality.

for such a low cost for lamps you do not have many options. i would just take a look around at some local retail stores and pick out a cheap tabletop lamp. or you could pick one of the swivel arm style lamps.