Learn English – customer-centered vs customer-centric

The first form sounds decidedly odd to me, but I can't see it meaning anything different to the second.

They both seem tautological anyway. Select means choose; I don't see the point in saying Choose a partner of your own choosing. I think just Choose a partner is simpler and better.

To convey that even making a choice is optional, say You may choose a partner [if you wish]

I'm not sure how many people would accept it as an "English" word, but gratis - without reward or consideration. comes to mind.

The more familiar, complimentary is often used the same way. Note that this is an adjective. Actual items are normally named (e.g. - a hotel offers complimentary breakfast), or collectively referred to as complimentary gifts. From the "trader's" side, such things may also be called corporate/promotional/business gifts/products; the recipients are more likely to call them freebies (or goody bags, which can be much more than candies for kids).

Gratis is more likely to be found in legal contexts (where you also find pro bono, used to describe work lawyers do without direct payment).

Complimentary is mostly used in commercial contexts where a trader provides something free, usually complementing (going together with) something else you're paying for. Note the different spelling for complimentary (something nice said or given), which many people get mixed up (that's 420 written instances of "complementary breakfast" written in error).