First question, do you WANT a viewfinder (that small screen you peep into)?

Second question, do you plan to EVER use an external flash?

If you said NO to both, save your dough for better lenses and get the A5100. It's probably the best camera in the smallest package I've ever seen (that has a large-ish sensor). It's also got a touchscreen and is very easy to work with.

If you said YES to any of the above, you're probably better off with the A6000. You have enough budget to get the kit, and that is good enough... at least to start with. The learning curve that comes with the A6000 CAN be a bit steep (if you wanna fully utilise it ler... if you don't you can always stick it in AUTO), but it's a very capable small camera.

Also another camera to consider, especially if you want something EVEN SMALLER: The RX100... at least one of the older models - the latest is quite expensive. Its got a smaller sensor than the mirrorless bunch (bigger than your phone though) but is infinitely more pocketable.

As for a normal DSLR... if you travel a lot the size and weight benefits of Mirrorless make DSLRs almost (almost) irrelevant. There are things that DSLRs STILL do better of course, but for normal travel and landscape purposes a full-sized DSLR is often overkill.

Just my 20 sens anyway.

Need to ask again on whether if FirstAidKit likes to take selfie or not. If yes, then a6000 might not be suitable for you. The screen cannot go 180 degrees.

Problems with DSLR - Heavier than mirrorless, sometimes more equipments to bring along too.

[An update - I ordered a messenger bag style camera bag + Newmowa charger/batteries as a spare. Will update again once I get them and start to use them.]

whats your budget?