Why not guitar? After all it seems to meet all your criteria.

I was also going to suggest a ukulele.

Cheap and portable - it outdoes the guitar in both respects. You can buy a usable uke for about £25 a pretty OK one for about £50 and a pretty good one for £100. I know, I've bought all three and still have 2 & 3. The first I gave to a charity shop.

The uke doesn't have the range of a guitar but it is much easier to get started - I know, I've tried both and I really love my uke but I never really got to grips with guitar.

That said either is an option. Both can be played chordally or single note style if you wish.

You could also consider a Mandolin, Bouzouki, Mandola, Cittern and even Banjo!

Whiskey in the Jar