I've been a full time W32 live aboard for about 9 years now. Maybe what I've found works for me can work for you. That said, as you settle in you will eventually sort it out for yourself.
Personally I prefer having things I need to cook with right handy. I'd think 'running all over the boat' to get an onion or a green pepper would get old quick.
Your mileage may vary but I don't buy more fruits/veggies than I can use in the next few days. I'm fortunate in that there are about a dozen open air veggie/fruit stands within a very short dinghy ride of my boat.
I have a small nylon net 'gear hammock' strung above the wet locker (next to nav station) to hold onions. I have another longer one strung under the boom gallows for larger items and/or those that won't ripen too quickly like pineapples, mangos, papayas, etc. (be careful of ants though).
I also have a small net 'ditty bag' for potatoes (don't store potatoes & onions together) hung from the inboard onion hammock hook. Same with my garlic that comes in it own little netbag.
Since my refrig works I store fresh veggies and fruits there. Otherwise if I were you I'd be looking at where to string small net hammocks in/around the galley. The trick is, finding one of the proper length you need for where you want to hang it although it's not hard to make a smaller one out of a long one. Or just hooks to hang net ditty bags from.
I have two collapsible double size 'milk crates' I bought from 'The Container Store'. They fit perfectly on the pilot berth (above the Starboard settee). In one I keep can goods and the other dry goods (flour, rice, sugar, etc.). A third is used for other 'random stuff'.
Collapsible crate
You always want to remove food items from their original paper & cardboard container. Roaches love cardboard and will lay eggs in them to later hatch in your boat. I store all dry goods in their own plastic jars/containers/Tupperware/etc and everything that won't go into a jar etc. goes into a zip lock bag. If necessary I will cut the instructions from the box and put it in the container as well. For flour, sugar, cornmeal etc. I use food grade screw top jars like these (you can find them at restaurant supply stores with different colored lids to 'color code' the contents)
Food grade jar
My final advice is to get your refrigerator running (and turn the Engel into a spare freezer). Using the icebox with block/crushed ice (as I did for a while) turns into a PITA. I finally replaced my defunct Adler Barbour unit only to discover the icebox insulation was shot and it only kept things 'cool'. I recently re-insulated the icebox I discovered what having lots of cold storage and an ice cold drink was about. Yes, it's expensive and a lot of work but bite the bullet. It's definitely worthwhile and will probably save your 'new adventure' in the long run :).