The common pet ants are
Lasius niger, which is your common black garden ant if you live in the US. However if you live in Europe, then it is probably a bad idea to go out and catch a black ant queen if you don't mind acid-spraying
Formica sp.. My first colony was
Formica fusca which is common in the US, but all
Formica sp. do spray formicarium acid, but they are a good starter colony to keep, as long as you have all nessicary things, Fluor for example, so they don't escape.
To find a queen you need to research times in the year for nuptial flights in your area. Nuptial flight is where queens go out and fly and breed. When you see a queen on the ground, it is probably fertilized and you could catch it to start your colony. ^-^
If you want to start ant-keeping, I suggest you go to a YouTube channel called AntsCanada and watch some of his tutorials; he is a professional and I watched him when I got my first colony and they're doing great!
Oh, I forgot to mention but, if you go to the AntsCanada website, you can buy queens with at least 1 worker, which garuntees fertilization!