I've had periodic redirects of search engines when I've installed software using the "typical" options button as these very often install or reset the default search engines. I've learned to always install anything as "custom install" and I un-check the various search engine, security, installer, and performance tune options. There are a lot of sneaky companies including the biggest.
In Firefox, the first thing to do is to have the search engine window visible (upper right) which should show the default engine > Gargle, Bling, Yazoot, FakeBook, Twizzle, or whatever. There is a small down arrow next to the search engine name > click on this arrow in the drop down menu click > "Manage Search Engines...". You can then then use the "Move Up / Move Down" control to put your preferred search engine at the top and when ever starting the browser, it will default start with the top listing. If you've acquired a search engine you don't want or seems reluctant to ever give up, there is the very useful "Remove" button. I've often had only one search engine in the list as others can be added instantly.
This the simplest method I know of and in my view worth trying first. I once had a weird malware/ redirector search engine "MyStart Incredibar" and all the un-install and registry editing in the world wouldn't prevent it until I used the "Manage Search Engine" technique and it was solved in 30 seconds.
See if that works, and let us know.