"should you decide"
uses the putative should that much more than its "equivalents" accentuates the character of chance happening to a certain potential situation.
A good compact reference on "should"
You should learn it all, for it is a very special verb, with a variety of meanings.
And yes, beside the BrE, it was quite in fashion in AmE at the end of the 19C and beginning of the 20C, with great writers such as Edith Wharton and Henry James (the latter, American born, a Briton by adoption) writing about the high-society, which seemed to use then a language with a certain British bent, something that seems to have disappeared since.
Now, in terms of using backshift to the past with "if you decide" instead of the /subjunctive mood/conditional/ "should you decide," you should be aware that this is frowned at by some people for certain verbs, and my impression is that this is the case for "decide," (see the other answers :-)), even though there are plenty of examples
"if you decided"
About 1,210,000 results
at Google Books, mainly applying to present/future time, say:
Bootstraps and Ladders: A Financial Outlook on Growth and ... - Page
Marcus Buford - 2012
If you decided to increase your saving practice to sixty dollars per month, in twelve months you would have $720 saved.
but also to past time, say:
The Anger Habit Workbook: Proven Principles to Calm the ... - Page 155
Carl Semmelroth - 2002
Perhaps at first, if you decided together to go to the movies, it felt
as if both of you wanted to go. After a while you began to feel that
Thus, I'd check the verb in question first a bit as to the applicability of the backshift to the past to it.