I would check deals vs places like Lowe's, etc. I don't think there's any particular reason to get them all in the same place apart from maybe financing deals or something. I have had good luck with Lowe's, terrible with Sears, but that's just my bias.
Ikea appliances are made by Whirlpool, so if you dig a bit and go look at both and check the feature charts you should be able to discern a rough Whirlpool equivalent and compare on price. Differences should mainly be cosmetic.
One thought that comes to mind that may or may not make a difference: other stores have longer experience with their appliance installers, which would be third-party contractors in the case of Lowe's, Ikea, etc. You might consider looking at an independent local dealer too. Sometimes they have equal prices, and in their case they may be doing the install themselves.
Appliance install would be after the cabinets, and it would be extremely unlikely (esp with a dishwasher) to have the same installer for all even if you get it all from Ikea. In fact unlike the home improvement stores I'm not sure they do any billing for installation, just recommending. Maybe that has changed recently.
Financing and delivery charges, too - might be cheaper to get them all on one truck than to pay for separate trips form separate stores. Might not be the dealbreaker - or maker! - but I'd try my hardest to compare all relevant fees since it sounds like the OP needs to be very cost conscious and those extras can make a big diff.
I used Ikea to redo a laundry room. Dealing with them made me certifiably crazy. The supposed "specialists" who have to put together the order over ordered many things and left others out requiring several extra trips of some distance.
When a faucet was broken, I think I had to spend at least an hour on the phone trying to make contact with an actual human being who was prepared to address the problem (I'm NOT exaggerating). They replaced the faucet but wouldn't do anything about the fact that I had to have a plumber a second time with an additional expense.
In the end, I saved a significant amount of money (which I made up in agita) and the cabs were fine for a laundry room. But I would NOT trust the customer response for an appliance. Mind you, the appliance might be just fine, but if you've spent a significant amount of money and it's not, they're going to make you wish you could just dispose of it and buy something else.