What should I expect to have to do to ensure a smooth purchase of my first Bitcoins?
Where are you buying your Bitcoin from?
In the Bitcoin Core software I found a receive tab. Under that I found 'request payment' In there I found;
-snip-
You don't have to use that feature. Basically all you have to do is press 'File' and go into 'Receiving addresses':
Pick one address from there (or generate a new one) and sent it to the person/service that you've buying Bitcoin from. That's it. You can check your balance on any block explorer later, e.g.
Blocktrail.