39-42 inches in front of fridge minimum. Cabinet depth fridge could help you. Eliminate or move assembly you show at the right of back door and position table up in that corner...this allows island to be shifted over , perhaps lengthened even. Try Different shape table.....rectangular ..running up/down in that zone.....So I would hold off on any built in to right of back door. Shift the table and shift the island so to have your improved walkway in front of fridge. I might put a mwave drawer or below counter microwave to gain back counter to right of fridge...I might consider a more medium sized single bowl deep clean up sink in a 30 in sink base ,[actually a 27 in sink is quite large] , centered in the island, and put a small bar sink in the corner on the perimeter...it can be snazzy looking and I believe it would get use!

I agree fridge needs more space. Counter depth fridge would be a good investment. I would do a single level island. Is the door required legally? If not, with the amount of money a remodel costs, it would be a relatively small additional cost to remove the door, or change it to a window. Then you have more flexibility with the layout.

Induction cooktops are wonderful, and yes a hood is needed IMO.

Good luck!

Never block the path to an exit door like that. That's a potential firecode issue if there isn’t a clear path. No, you don’t need to close it up. That’s also a fire code issue. You have to have a secondary exit. Not a unless you put another door in the eating area.

Like maybe replace the built in with a nice sliding patio door. Access to the rear from the kitchen is always needed. How do you take things in and out to grill otherwise?

Maybe omit the pantry cabinet and put the micro elsewhere and put the range on that wall? Omit the wall on the left of the refrigerator or move to gain more space on the wall?

strongly suggest single single level counter.

what is behind fridge, can you steal some space behind so you can recess it into wall?

do you have to keep backdoor for fire egress? If not, just leave it on the outside - sort of. Leave it in, but inside make it invisible.

Also, since that is an exterior wall, why are there no other windows on it? There no connection to the exterior anywhere here. That’s just a poor design that doesn’t consider that.

Post the the rest of the house that surrounds the kitchen, and the cardinal directions of the house.

with tight budget you must discriminate. you can have things done in phases. Split levels have challenges.....If you have no connection except small door to outdoors you may want to consider this issue initially, rather than removing interior walls/and sole focus on kitchen right now. Homes with windows/sliding or French doors/light and access to patios/decks/yards enhance living, provide resale. As said, post more, and orientation of things/access in/out and adjacent spaces. There is nothing wrong with replacing what you have w Ikea...or just improving what is critical ......or leaving a working kitchen to do other improvements your whole family will enjoy over a long time.....and come back to kitchen.....split levels sometimes need some infrastructure adjustments. This is not to discourage you re: the kitchen, but encourage a fearless and creative look at some basic/important details of your home.

Do you have a deck off that door?

The south side of the house has the most desirable light. I’d recommend pausing thinking about just the kitchen, and think about the house as a whole. Think of how to get much more of that desirable light into the whole house. Think about a deck or patio space with French doors going out. Think about traffic flow through the entire house.

I know expenses are tight, but it would be really nice if you could add a window in the dining area and reuse the salvaged brick to cover the bottom of the door opening and make the top half a window to match your other window. Then your stove would look great there.

As suggested, I would also trade the pantry and fridge. It will not feel as constricted in front of the fridge.