My answer focuses on the header question about decades—which is the question that most readers will probably expect to find answers to here. With regard to decades expressed in numerals rather than spelled out in letters, some style guides recommend omitting an apostrophe, while others recommend including it. For example, from The Chicago Manual of Style, fifteenth edition (2003):
9.37 Decades. Decades are either spelled out (as long as the century is clear) and lowercased or expressed in numerals. No apostrophe appears between the year and the s.
the nineties
the 1980s and 1990s (or, less formally, the 1980s and '90s)
The Associated Press Stylebook (2002) adopts a rule very similar to Chicago's:
decades Use Arabic figures to indicate decades of history. Use an apostrophe to indicate numerals that are left out; show plural by adding the letter s: the 1890s, the '90s, the Gay '90s, the 1920s, the mid-1930s.
The Oxford Guide to Style (2002), while differing with Chicago and AP on capitalizing the spelled-out decade name (Oxford University Press prefers this) and on using abbreviations like '60s (OUP condemns this), agrees with Chicago that the plural numeral form should be spelled without an apostrophe before the s:
To denote simple ten-year spans OUP style prefers, for example, 1920s or 1960s to nineteen-twenties or nineteen-sixties. To denote decades of a specific character (say, the Roaring Twenties, the Swinging Sixties) OUP prefers Twenties or Sixties to '20s or '60s.
But Words into Type, third edition (1974) takes the opposing view:
In referring to decades, the sixties or the 1960's is generally preferred (not '60's, '60s, 60's, or 60s; the last form is used occasionally for ages of persons).
The New York Times Manual of Style and Usage (1999) agrees with Words into Type about the apostrophe, although about little else:
decades should usually be given in numerals: the 1990's; the mid-1970's; the 90's. But when a decade begins a sentence it must be spelled out. [example omitted]; often that is reason enough to recast the sentence.
Clearly the question of how to render a particular decade in print is a style issue on which reasonable style guides may differ. Follow the one you have to follow, or choose the one you like.
And links two things (e.g. a classmate and I), and results in a plural subject (A classmate = 1, I = 1, so a classmate and I = 1 + 1 = 2), so were is correct:
Awarded such and such scholarship in 2011. A classmate and I were the first students from my college to be awarded this scholarship.
The rule you refer to applies only to figuring what case of pronoun to use (e.g. I or me), not to whether you should use singular or plural (e.g. was or were). When you use the rule to figure out which of I or me is correct, you should alter the number of the verb (were becomes was) and direct object (students becomes student) when you take out the other person:
A classmate and I were the first students becomes I was the first student (correct).
A classmate and me were the first students becomes Me was the first student (incorrect).
When you add the classmate back into the sentence, you can be assured of the proper pronoun (I, not me).
Best Answer
I feel that this may well be a duplicate, but I can't discover an original.
These Google Ngrams show that decades are used with singular or plural agreement. They're essentially collective nouns for the years they contain. At least in the UK, referring to the Thirties say (and notice that the noun is often regarded as a proper name) and having in mind the complete time interval would be regarded as looking at a single interval, and be used with a singular-form verb:
Sometimes, proximity agreement sounds far more natural:
I agree that the more logical 'The Sixties was the best decade ever' sounds rather unnatural, so I'd rephrase.