Try Firefox, from mozilla.org. Free and awesome, you will never get a bookmark unless you put it there. Very user-friendly interface with a ton of privacy features and personalizations
I use Chrome. The only bookmarks present are the ones I put there myself.
ETA: Probably the best strategy at this point is a little experimentation:
1. Make a note of one or two of the unwanted bookmarks you noticed today.
2. Make a note of the steps you took to delete them.
3. Tomorrow, note whether any new unwanted bookmarks have appeared.
4a. If not, that's your high score - 1 Day. Try to beat it : )
4b. If you do notice more unwanted bookmarks tomorrow, make a note of them.
- Are they the same as the ones you deleted yesterday?
- Are they bookmarks for sites you've visited recently, or might have visited recently?
Bonus experiment: There should be a direct causal relationship, between clicking the "star" icon at the rightmost end of the Chrome address bar, and the creation of a new bookmark. Test this by clicking on the star, and making a note of what happens. You should get a small prompt, to choose the name and location of the bookmark, and confirm or cancel it. The star should also change from a hollow shape to a solid shape in the address bar. Is this what actually happens?