Yeah, the planet in the beginning was Earth.
As for the different looking Aliens in the later films, I figured they are just more
refined version. The incident on the planet they go to took place some 2000 years
ago, so they've had plenty of time to improve on the alien maybe on other planets.
Of course, the look of the actual full grown alien has to do with the DNA of the
host it's born off. Humans give birth to the larger drone & warrior types and in
Alien³ we have the slimmer, faster runner alien from dog (or ox if you go with the Assembly Cut).