For the FamilyTreeDNA.com yDNA tests, if you are pretty confident you are going to buy the Big Y test, would that fill in your SNPs up to yDNA-111 if you had only purchased yDNA-37 before upgrading to Big Y? If so, then it would seem like it is more efficient to only buy yDNA-37 before going to Big Y.
I think there is still value to upgrading beyond Y37 (to at least 67) even if you are 100% confident you are going to do a BigY.
Short version: You get near term genealogical value matching with Y67+ matches.
This may change as more BigY's are done (they have only been out 2-3 years) and the tools around it improve, but as of May 2016 this is my position.
1) Y37 I personally put little value on for near term genealogical purposes because of the number of generations of accuracy you are talking about. I always say get at least a Y67 but I usually spend the extra and get a Y111. Why I do this is because I know most will not be purchasing a BigY and it is a lot easier to convince someone to upgrade from a Y37 to a Y67 or a Y111 than a BigY from any Y level. So if matching is of any importance get at least a Y67.
2) FamilyTreeDNA's "Match" criteria for BigY is VERY highly criticized and hard to understand. From my current understanding having done about 10 BigY tests for individuals now; it basically considers anyone in your major Haplogroup subclade a match, even if they are in a completely different branch of the subclade. So for genealogical purposes, except for the most advanced DNA users, using BigY by itself is not very useful.
3) The BigY provides additional detail / granularity the Y111 just cannot provide in terms of Haplogroup.. but generational difference calculation math is still a developing science on the BigY so no nice matching numbers or calculations. The STRs in Y111 are present in every individual male; where particular SNPs detected by BigY are not always present (see #5 below also). As I also understand it, each STR in a Y111 is fairly well defined and a lot known about it and each individual STRs mutation rate and values are known. This allows for a fairly consistent and comparable test to be performed across a large population base.
4) I trust YFull's ever evolving match criteria and grouping much more than FamilyTreeDNA's BigY criteria at this point but the pool of people having submitted their results from FullGenomes and ftDNA's BigY is still less than 10,000. There are many many more individuals that have taken YDNA tests, even at the Y111 level this number is probably in the 10s of thousands.
5) BigY tests are not a prescribed test reading specific markers (SNPs); but more a detection test of if something is present or not and if so what its value is. Thus one of the criticisms of the BigY test with all of the data is does collection (the .BAM file being 400-900 megs) is the inconsistent data generated from them and simply people feel SNPs are sometimes missed. FamilyTreeDNA admits this occurs and is one reason they also recommend SNP packs on top of BigY tests. SNP packs are prescribed tests like the Y111. I believe the resolution my BigY tests have been coming back at is about 40-50x; Full Genomes offers a much higher resolution Full Genome test that you also get a mtDNA out of.. but is only useful for YFull.. you cannot transfer it anywhere else.