IC Recommendations

1. Do you know what is an "analog IC"?
2. Do you know some of the various functions they can perform?
3. Does your flyer have a list of ICs that are free?
4. Do you have some projects in mind you'd like to build, test, and use?
5. Have you performed any searches using the search terms "analog ICs"?

Here’s a museum website that includes the very first analog Ics. Imagine that!
http://www.computerhistory.org/revolution/digital-logic/12/281

One manufacturer with some examples of types of analog circuit applications:
http://www.aldinc.com/ald_standardprod.php

 

Around here there's no such thing as free, and flyers like that always have some kind of catch (like gotta buy something else at inflated prices or sign up for something etc).

But if this deal is legit in your case then I'd start with a couple of things that are useful for many different projects. Linear regulators and op-amps would probably top the list of things I like to have on hand as basic parts for simple projects.

 

The world of analog chips is so broad that I seldom keep many on hand any more. If someone DID let me run free in the Ti catalog, I'd probably pick up some OPA2604's (Amazing op amp), a couple of INA118 (Pretty good instrument amp), a couple of chopper stabilized amps (maybe OPA4188), and some good general purpose instrument amps (OPA277), and probably a couple of precision CMOS amps as well.

 

IC manufacturers (or their distributors to be specific) are usually willing to give out free samples to customers for prototyping or students for projects. The idea being that you'd eventually order them in manufacturing quantities or you'll think of the brand once you get into industry.

That being said, I'd just shoot for the most expensive thing you can :) . Of course, make it something useful. If you're not in a hurry, I'd just order a couple of things that seem interesting to you and then asking for 20 of the ones you like best.

I hate to reiterate this point because it sounds like I'm being greedy, but analog ICs are generally pretty cheap, so I'd try and go for something that is actually expensive and you wouldn't normally get the chance to play around with a bunch. These look really nice.
http://www.ti.com/lit/ds/sgls145b/sgls145b.pdf