Interesting thread.
For me, it varies, which makes it kind of hard for me to answer this. Being able to use my phone one handed is important and nice for me to have. I like the small phone size factor quite a bit, but everything else just has to work.
1. Accessories - I really don't care about this at all, pretty minimalist lol
2. Expandable storage or fixed - Indifferent really, two of my three phones have fixed storage.
3. Storage - I care about this, but not as much as the people who cry out that 16gb isn't enough for a smartphone in 2016.
4. Ecosystem - As someone who goes between OSes when I feel like it, I care, but it's hard to be a loyalist since I have things I love and hate about all three of the platforms. Not counting BB, sorry.
5. Screen Size - 5.2" is my limit, but 4" is not too small for me at all. 4"-5.2" basically.
6. Front facing camera - I like to take selfies occasionally when I'm in the mood to, so this is important. It's kind of why I have a hard time with the Lumia 640 FFC in non daylight, I'm spoiled by my other phones.
7. Screen resolution - No WVGA or anything of that nature for me. It's either 720p or 1080p. Anything lower, I'll pass, always.
8. Main Camera capabilities - Again, I like to take pictures occasionally, and having a decent camera is ideal so that I can always get the shots I want.
9 (see below)
10. Battery life - Nothing annoys me more than a phone with terrible battery life. Let me have a day at the minimum and I will be fine.
Other things? Both of these are tied for 9.
-Customization: A phone that lacks this kind of makes me feel like I can't fully express myself. (Yeah, it might be sad that I feel that way about a phone, but eh.) This is the same girl that LOVES her green shell on her Lumia, and the Mint of my Nextbit Robin.
-Simplicity: I really value this, regardless of it is the illusion or the actual deal. Anything that feels like it is just too much and overwhelming out the gate, I'm less likely to feel okay with the phone. I really don't always want to be the person who is always tinkering with their phone.
Funnily enough, this thread has made me realize why I have been restless with my trying of phones. I desire a phone that packs 9 and 10 together for me, provided that it has the apps that I need and I'm used to. Everything else, I can generally get from whatever phone I (have) decide(d) to try.