Phil is more knowledgeable than me, so see what he thinks, but in my very limited experience the Y dna test has been of no use whatsoever, so you may find it is an expensive gamble especially for a non direct ancestor.
Yes, it depends what you are hoping to achieve. For the greatest chance of matching and finding living relatives, which combined with traditional research can hopefully prove your ancestral descent through most recent common ancestors (those people from whom both you and your match are descended) it has to be an autosomal test every time.
Y-DNA can only be used to investigate the direct male line of your ancestry. It may help for instance if you are unsure of your father's ancestry. It is also useful if you want to research more distant aspects of that line and become involved in a one-name study for your paternal lineage. It might help break a brick wall in that line, but expect the results from a close relative matching point of view to be very disappointing, generally.
In that sense I was very lucky, I have one 67 marker match who is my 2C1R, but I already knew about him since I already had an autosomal match to his sister. All my other matches are at much lower levels and relatively so distant that there is very little chance of finding an MRCA within a reasonable timeframe, if at all. But one thing the Y-DNA markers can do is to cluster those individuals so that you know which are more recently related to you, and which are more distant.
My surname group is heavily US biased, and very few of them have any idea at all of the identity of their British or European ancestors.
Although to put that in context, I knew nothing about my paternal GF's origins when I started researching. He was an orphan whose parents died before he was 3 years old. It took me many months of researching and comparing records and contacting possible relatives to identify his parents. My single Y-DNA 2C1R match would have shortened that process considerably, but as I say, I think I was in a sense very lucky to find that match via a Y-DNA test. Most people who test will not get a single match at such a close level, and by the time I did, I had already confirmed my suspicions through autosomal testing anyway.