Good cardiovascular condition, and a nimble mind.
I’m of the old “masked mystery man” school.
(And technically, there are Real Life Superheroes who are a little iffy on one or both of* those.*)
The old 6 Million Dollar Man, plus modern body armor, is about the lower limit.
Basic FISS for me. I’d also need a better attention span.
Technically, “extraordinary luck” has been used as a superpower in some comics—or variants of it, as in “probability manipulation” or “cause bad luck for opponents.” Considering what I’ve seen and read over the years about various man-made disasters, assassination attempts (both failed and successful), bizarre coincidences, and miraculous escapes, having life be consistently improbable in your favor might be the most subtle but powerful power you could ever have. Or need.
Shapeshifting. I need to be able to get into a wide variety of places to catch not just common street criminals, but real criminals with serious effects on society, and for that, shapeshifting is probably better than a lot of other powers. Not just shapeshifting into other humanoid forms, mind you, but more the ability to change shape into literally anything, from small to large, and made of any material without particular regard to the physics of it and things like the square-cube law. The shapeshifting should also make me relatively difficult to damage - any damage I suffer I can just shift to repair, and if I don’t want to be vulnerable at all, shift into something that can’t be damaged.
Telepathy/Mind Reading. To go along with the shapeshifting, I’ll need to be able to know what people expect of someone who looks like whatever I’ve chosen to disguise myself as, so being able to read their minds for this purpose is key. It’ll also help me discern who’s really a bad guy and who’s not. And in addition to that, give this power the ability to duplicate skills from other people. If someone else knows how to do something, I can telepathically ‘scan’ them and then have all that knowledge and be able to fully apply it myself. This way I can build up skills needed to take out cyber criminals, embezzlers, people like that.
To minimize as per the OP, you could maybe get by with just Mind Control: why read a guy’s mind when he’ll willingly explain stuff on command – and then, on command, forget he just did so? And why shapeshift into someone’s lookalike to duplicate his skills when that looker already (a) has those skills and (b) works for you?
Mm. I’d actually consider mind control a more powerful ability than those I listed. I suppose if the limitation was on number of powers, mind control would probably do it, but if it’s on how powerful those powers are, I think mind control is actually stronger.
Also, without the shapeshifting (and thus the relative immunity to most harm) I think I would likely be too timid to make an effective superhero, even (especially) with mind control. I would be more likely to use other people to do any necessary fighting, something that doesn’t seem all that heroic.
Didn’t want to hijack this with a quibble, but since the thread went dormant for the last day or two let me nitpick a bit. 
I mean, really look at that package deal: you start off with “relative immunity to most harm” – “if I don’t want to be vulnerable at all, shift into something that can’t be damaged” – which was already enough to satisfy Trinopus (who thinks mere invulnerability would do it), sure as Scumpup spells out that 1938-Superman-esque toughness means he doesn’t figure on needing superhuman strength and speed so long as he’s got nightvision…
…except you’re getting it as one aspect of the power to “change shape into literally anything, from small to large, and made of any material without particular regard to the physics of it and things like the square-cube law.” So you can shrink down to sneak around and spy on the bad guys, or grow to giant-size to deliver a superstrong beatdown in perfect defiance of said square-cube law – either of which is enough for heroes in the comics, and both of which work well together…
…and that’s all included with the super-useful Disguise Yourself As Anyone power, which (a) is distinct from growing and shrinking and being inhumanly tough, but which (b) is a subset of also turning into non-humanoid animals and so on. That’s a lot of power from one ability even before adding mind-reading.
And me, I just want the hypnotic voice that – I dunno, maybe just works on one person at a time, even.