Just two thoughts:
One: think about utilizing your side yard. Most side yards are wastelands anyway and with appropriate fencing can be made into an attractive spot for a shed that won't become the dominant feature in your backyard (because, trust me, most sheds are UGLY and BIG and make an awful lot of themselves). Side yards will need two sets of fencing; one between the front yard and the shed and another between the back yard and the shed.
Two: if your whole yard is only 125 feet wide, you might be better off paying someone to mow it, and not putting up sheds to house the expensive equipment. Sell the mower and put the money into regular maintenance.
Good luck with your project.

That is a good point about hiring someone to mow for us. But we are gardeners who like to be outside. Our yard is 2/3 of an acre, which is small in many parts of the country but middling to large here. I used to think I wanted 5+ acres but heck, I flew 100k miles last year for work (I'm not a flight attendant) so there's no way I could manage it. What I'm saying is, I don't have a lot of time to garden but I like to do it when I can, and having to drag all the stuff in and out of the basement is getting really old.

So, we will need to have a shed for the tree cutting/trimming equipment and all the long-handled tools (feels like a hundred, but probably only 30-40 of them).

Our side yard isn't much of an option because it's sort of an extension of our front yard, it's pretty :) I think I might try to talk DH into a single 8'x12' shed for the mower & snow blower, and have something like this built for the long-handled tools & such:

http://homerefurbers.com/projects/151

So I think more information is needed regarding the actual lot layout, since that is what drives whether the large (meaning really large) shed is do-able in a pleasing way. As woodyoak said, usually, but not always, a larger structure is more flexible in how you can design the space--you can do just about anything if you re-jigger the interior for it, whereas with the smaller structure may always be something that doesn't fit, or getting in and out is a pain, plus if you do only one structure you may tend to do it up right, with the types of doors and windows that are nicest, and it is the type of structure that can become the cute garden cottage and so forth. That said, it can be more functional to have 2 sheds if you organize them more seasonally, if one is closer to where do more of the work, if the locations "save" your prime space that would be used for the larger shed. So I think it's a layout-doodle thing to get the feel for where they would go, whether if you do 2 they have to "match," or can be different sizes and dimensions according to where they are in the yard and what their functions are (a tool closet can be done differently from something that has to hold mowers and such, and smaller structures can get away with looking more utilitarian or rustic). 12 x 16 is a pretty big shed, and I agree that you would want something that big to look like it's a planned carriage house or something and not a shack. Also 5 feet from fence, if that means must be 5 ', wastes the space behind. So can't tell whether it's possible to site the larger one so that the larger 15' fence setback becomes a pleasant usable space-- a destination--rather than just sucking up 15'.

Our lot is much smaller than yours at 75x150. We built a garden shed/workshop near one corner of the yard. It's about 5' from the rear property line. We use the space behind the shed to hang ladders and pieces of wood. There's a small Suncraft shed on the side where dh stores the mower and gas cans. It's not visible from the house or screened porch.

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WoodyOak and Natal- Your sheds are adorable. I want my husband to build one for a playhouse/garden retreat next summer and am collecting ideas for inspiration. Thanks for posting your pictures!