Post payment on direct buys is something I hear for the 1st time. Maybe if you have a long lasting partnership you could be allowed such thing.
You should check adnetworks such as FB or GDN, they work on post-pay, but initial spending treshholds are low (20-25$/€). Over time (and successful payments) you can get that treshhold amount increased and post-pay for your ads.
Also, judging the way you ask your question "what would be a good site to put ads on" ---> digital media buying is highly competitive field, with some of the best players playing on it, I'd highly recommend you to further educate yourself, get a better understanding of how all of this works, before spending even $1 on paid media.
As of "how its usually done" - you contact the website, if it's a larger one you ask to speak to their advertising department. You make a deal, and you send your banners which might have some requirements as of size/type/etc. Some website have self-serving platforms where you can upload your ads, but those are rare. The invoices are called Insertion Orders. Tricky part on direct buys is where the banner will be hosted, you might be given the chance to use your own server and just provide the iframe of the banner so that you can check your numbers, but that' a bit advanced.
A courtesy tip - 90%+ of media buying campaigns are failures, if you don't know what you are doing chances are you will end up losing money. Recommended initial budget for beginner media buyer is 3-4k$+.
