Just make sure when you remove the carpet, that if there is adhesives, that you get it all up, or you will see those spots through the stain. A colored epoxy would cover it better, but you still need to remove as much adhesives as possible. You can epoxy or acid stain right up to the tile or vinyl, and use a small threshold for the transition. We did this in many places, and it really flowed well together.
Be aware to that if you have to do any patching (the acid stain will highlight that as well). If you do want to go acid stain, and you do have patched areas and adhesives left, you can always put down a skim coat first, then stain, which will give you a more consistent look.
Let me know if you have any other questions.