Hi, welcome to the world of kitchen renovation.

I'm pretty sure I know the condos of which you speak. Not your unit, of course, but I've been there when I lived in the area and had several friends who lived in those condos. There's not much you can do about the layout of the kitchen unless you want to start taking down walls. Sounds like that would be over your budget, and I would strongly recommend sticking to your budget (I didn't and it's painful). Plus, the layout of those units works pretty well.

I would suggest that you reconsider getting rid of the existing cabinets. They are obviously solid and well-built if they have lasted 40 years. No Ikea or Home Depot cabinets will last 40 years! Refinishing or repainting, and replacing the hinges where needed and the hardware will look great. Also keeps stuff out of landfill, yadda yadda. Find out where that mold smell is coming from--it might not be from the cabinets. It might be from a leaking pipe that should be fixed.

Do the ceiling. Lighting makes so much difference! While you're at it, definitely install under-counter lights. Not the Ikea ones, but hardwired ones. You will need an electrician. He or she should also make sure that everything meets code, including GFI outlets. It's important to have permits in place and inspections passed for when you sell the place.

I'm rambling a bit but here's what I would do:

ceiling with recessed lights on a dimmer. Makes a huge improvement
under counter lights (PM me for my brand--I'll look it up if you want)
refinish/paint/new hardware on cabinets if they are solid
new sink, or at least new faucet. Huge difference.
Disposal if you don't already have one. Good for resale
countertop--I don't know what yours is. Mine is concrete and I love it.
tile backsplash. I have yet to do this in my kitchen!!! Winter project, perhaps (wasn't that supposed to be last winter's project?)

One of the reasons I encourage you to keep the cabinets is that unless you are going to get really good quality cabinets, they are just going to look cheap and won't hold up. Ikea stuff looks good, but after a few years, it starts to break. I have custom bamboo cabinets that I love, although they are very expensive. My kitchen had no cabinets, so I was starting from scratch. If you sell the place, good quality cabinets will really be a selling point. If you stay, you will enjoy really good quality cabinets (with self closing drawers--ooooh).

appliances: replace as needed. Not necessary to do all at once, unless you don't have any to begin with (like me). But that's not your case.

Remember, have fun! PM me for more questions if you want.