I asked a question, Grub forcing me to boot from flash drive and rapidly got a great answer that solved the problem. I upvoted the answer, but there's no check mark for me to mark that I accepted the answer. Is this because this is my first question in "Ask Ubuntu?" as opposed to the other exchanges?
The response that you are calling an answer in this case is really a comment. Comments can be "upvoted", but aren't considered answers.
If the comment alone was sufficient to answer your question, then the normal course of action would be to @reply to user who posted the comment and ask them to convert it to an actual answer so that you could accept it.
However, in this case, the comment linked to another answer here on Ask Ubuntu. That means that in reality, we should likely mark your question as a duplicate of the other question. Closing a question as a duplicate isn't a bad thing. It can even serve as a useful "signpost" for others who find your question through search, which leads to the other question (and its answers).
If you'd like, I believe you can even Flag your own question (since you have enough Rep from other Stack sites) as a duplicate of the other question. You should then be able to accept your own duplicate proposal (via the header).
I've actually done this myself at one point here on Meta, when I posted a question and then found that it was a duplicate of an older question.
Is this because this is my first question in "Ask Ubuntu?"
Nope! You've actually already asked a question here that had an answer that you marked as accepted!