Is it better to choose a role that you would like to have when preparing for an audition or is it best to just do your best at the audition and wish for the best when it comes to casting?

I'm a theatre major at a general university, not an arts school. As a theatre major, I have to audition for every show in our season. There are four shows per season: a musical, a revue, and two plays. My professor usually picks shows that are comedic while I like shows that are dramatic and deep. Our musical last year was Guys and Dolls that I was a part of and this year we are doing Once Upon a Mattress as our musical. I don't care for the show and find it quite stupid honestly. I know I need to have a positive attitude about every show I could possibly be a part of or it will throw me off with everything. I need to show my professor that I'm continually progressing in my acting craft. I'm a bass so there probably isn't any roles that would fit me. I have watched the 2005 Disney movie and have the Original Broadway Cast Recording. We can sing a song from the show for our audition piece but I did that for Guys and Dolls and don't want to do it again. I was thinking of choosing something by Rodgers and Hammerstein because of the same quality of writing styles. The only music I know from an R&H show is The Sound of Music. I need help on a song choice. I have the summer to prepare for this audition. If you could get me any help, anything would be appreciated. Thanks!

Interesting question and one that's come up for me in the past.

My take on it essentially comes down to "how much do I want to be in this show?" versus "How much do I want this part?"

There's a continuum between "I want to do this show and really don't care what part I'm in" (though I may recognize I'm better suited for one or several parts than for others) [for me, that'd be something like "Avenue Q"] and "Frankly, I just want to play part X, and otherwise I don't really care to be in it (for me, that'd be like playing Don Q in "Man of La Mancha"). The closer you are to the AvenueQ side, don't worry about specifics, just show off. But if you're near the MoLM side, tailor your audition to the part.