Without a screenshot it is hard to tell what css styling is affecting the buttons, so it is difficult to say which css you should add or change.
I have had a quick look at YouJoomla which is where you go the template Baseline. They have a custom.css file where you add code. I do not think you can create a custom.less file, though I am not a member so have no access to such extra info... You could add css to style classes that relate to your template ie .inputbox is a class used by your template for the input on the search page of the YouJoomla Baseline demo site... I might consider creating a Seblod position and/or variation override, muck around with typography etc and add classes like .inputbox there.
I have added an image, adding something like this to your forum post could help someone answer you more specifically. Unfortunately though, I haven't mastered the technique of adding screenshots that are readable, they get compressed a little too much on this forum, oh well.
Tutorials and forum posts hold the answer, plus check out css-tricks, Chris Coyier is a legend!!!
@ Bucklash You have said it all; the lasting solution will take highly skilled CSS to accomplish. This is beyond my capabilities at the moment.
However, I found work around. Instead of using the search module, I created my search elements using the List & Search type and with the aid of template positioning the elements where aligned as intended.