Congrats on getting a new shop space!
For the Break Away season, we moved into a new shop space (A loft in downtown St. Paul) that had been completely renovated for us. We kept the layout big and open for the shop area, but had a section area for programming, PR, and meals walled off with windows into the shop area (the windows help the team feel like a whole team, instead of breaking off into subgroups that never see each other). There was a dedicated space for storage (We found some Home Depot-style shelving real cheap on Craig's List). We kept the machining tools in one area, with final assembly in another, 5 or so feet away - you want to be able to provide supervision over the tool usage easily.
After the season was over this year, we got to move into our brand new build space in the school. This we literally got to design from scratch - it was an addition to the school, not a remodel.
In designing this space, there was a lot we wanted to consider:
1. Noise: The machine tools can be loud. We wanted the "Machine Shop" separated from the assembly area, so we could close the doors to keep noise down.
2. Power: We wanted to make sure we had sufficient power for our needs, while maintaining safety. This resulted in a master safety switch in the shop that, when pressed, cuts power to every machine in the room. This way we don't have to run past people or dart in near a machine if we see something unsafe happening. We also made sure we had outlets spaced/located where we wanted them, according to our floor plan. If that wasn't enough, we have power drops in the ceiling as well - they're dangling from spring-loaded lockable reels, so the outlet can be stored above head height, but when pulled out can reach all the way to the floor
3. dust collection: When using machine tools, a lot of dust is generated. In the end, we ended up without a built-in dust collection system due to complexity and the need to support both wood and metal. Instead, we're still using the shop-vac for dust collection.
4. compressed air: We designed in an exterior compressor that has a line running into the build space. This way we have the benefits of compressed air, without the loud compressor in the room
5. Tall ceilings: Our old build space had 11 foot ceilings, which isn't really quite tall enough. The new one has massive ceilings that I hope we'll never have a need to hit

6. Loading bay: We have an insulated garage door in the assembly room. This lets us back the trailer fully into the room for loading/unloading, which is really great in Feb/Mar! It also gives us as much room as we need to load stuff in and out of the area.
7. Carpet on the practice area! Our practice area is a little bigger than a half-field sized room, carpeted, which doubles as a classroom. All of the desks/chairs are on wheels, which makes it pretty quick to clear out the room for driver practice
8. Extra rooms: We have a dedicated conference room with a table, seats for 12, 3 white boards, and a large screen TV we can hook the laptops up to. We also have a dedicated Lego League room with adjustable height tables and room for several groups to work.
For spacing on equipment, use common sense or look for guidance from the manufacturer. Space things out far enough that you won't be bumping elbows, and so your parts can fit (for example, you'll often use a band saw to cut through 12 foot long square tubing) without too much hassle. Leave room to walk, so people can walk behind others that are using the tools.