Sure fire way to sort out the Democrats and Republicans?
For ME,
1) Style and Function: I want it to look good, look good with it's surroundings, and I want it to FIT me. (dishwashers have racks I like, Fridge has shelves I like, etc). Not everybody has this choice though.
There was a time when I'd have taken a free refrigerator, regardless of looks or age, just as long as it worked.

2) Price: I still remember those free/ugly/working days. I can probably go out and buy any fridge out there, but, being able to do so, and being able to "afford" it are two different things.
So.....PRICE: Given same / same / same / same...I'll choose the least expensive one most every time.

3) Reviews: I fully understand that NOBODY gets on the internet with nothing better to do than leave a review telling how great their appliance is.
Most reviews come from people that are on the internet, trying to figure out what's wrong with their appliance, and seeing if anybody else has had the same problems.
AND...You'll find 5 reviews on an appliance that 20,000 were sold.
But, I do look and this does somewhat affect my decision.

WARRANTY: Yep, darn near last. If you really get down to the fine print, many warranties, and store extended warranties don't really cover much. My touchpad on my oven went out in 14months. I bought the extended coverage at an extra cost. OH, sorry, that does not cover the touchpad. It only covers stuff that doesn't break or wear out.
I look for the factory/manufacturer warranty, for the longest duration on PARTS (not labor). I'm fairly proficient at parts removal, replacement, and just generally screwing up most anything. So, if I can just get free parts? I'm good.
Although, I don't usually expect even that.
I just take it upon myself to get a decent deal to begin with, and save the extra money for repairs down the road..if needed.

Availability of competent service where you live. This obviously is less of a concern for those living in a large metro area, or if you're buying a popular brand appliance made by the dominant manufacturer of that specific item.

But the farther away from a big city you live, and the farther from standard an appliance (or its manufacturer) is, the more important it is to find out in advance where you'll get service for your appliance in your local area when needed.

The coolest looking appliance may seem a lot less appealing if you learn that getting service means carting it several hundred miles away.

1) Value. Not price necessarily but what am I getting for my money.

2) Performance. The flat out ability to do the job it was intended to do.

3) Country of Origin. I am not buying an appliance from a company headquarted in the third world. Made in third world by first world company? Maybe. All else being equal, I will buy American.

4) Reputation. Reputation of manufacturer and reputation for the particular appliance. Part of that is my circle of friends,reviews on GW and similar sites, and JD Powers. I used to give Consumer Reports some weight but have fallen so far I no longer care what they say. CR is so out of whack with every other source and my personal experience that I have given up on them.

5) Style. Cooks over looks. I do care somewhat what an appliance looks like but not top priority.

6) Noise. I am not hyper noise sensitive but don't want a racket in my kitchen either.

7) Efficiency. Water and Electric efficiency.

8) Warranty. I prefer a longer warranty to a shorter one but appliances rarely fail in-warranty. It seems manufactures know how long something will last and give you a warranty just short of it. And as Dando says then there is the fine print.

"choose who to buy from".

I'll assume therefore that the decision as to which unit has already been made.

1. how well can they service the unit. Do they have factory trained staff? Are they factory distributors? Is there warrantee work covered by them or a 3rd party?
2. Stock on hand? or do they have to order X weeks out?
3. Price.
4. Price.
5. Price.

sorry I should clarify my question. Weedmeister got it right, I'm assuming you have decided what you want to purchase, but you're choosing who to buy from.

Thanks for the quick responses so far!