Based on my recent experience I can recommend at least for your short-list (or as an addition given the comments above which seem to suggest you can get all in one except the deep-fry part), the Tefal Actifry.
Replaces a deep-fat fryer and can do most of the things you can do in an oven and stove-top, and when frying it uses only the amount of oil that's left on the food at the end (i.e. about a tablespoon to do say a kilo of chips).
But also does quite a lot besides the obvious chips and meaty things like hot-wings and sausages; some examples posted here: http://www.lakeland.co.uk/L?content=noticeboard/recipes/actifry.htm (stews, curries, fried rice etc)
Some reviews have posted concerns about reliability (clips break, fans burn out), which are supposedly fixed in more recent iterations of the design (users reporting that replacement lids have thicker clips; 'Which' a consumer group in the UK has a response from Tefal saying they've fixed the fan issue..), but to guarantee I had one of the newer models I went for the only-recently introduced 'Family' version which also has 1.5x the capacity of the original model. No issues so far, but I've only had it a few weeks..
Overall got it probably mainly as I just generally have a weakness for gadgets, but it's proved a great/very versatile addition to my tiny corner-of-the-studio-flat kitchen and my friends are loving the chips it makes :) And when cooking just for myself I also really like the way you can set the timer and go watch TV while it does its thing..