Don't forget to undo the stitch that holds the jacket vents closed, if you buy the suit. Keeping the jacket's side pockets basted closed is at least arguably defensible, but the jacket vents are another story. I mention this, as I have, in fact, seen men wear very nice new suits in which such vent stitches had not been removed. Hey, details matter.
Anyway, the sleeves are too short. Shortening sleeves is usually a "See Spot run" sort of alteration - very basic and affordable, yielding good results. (Yeah, if the sleeve has functional buttonholes, it gets more complicated. Still, let's not confuse the point by talking about the small fraction of sleeve shortenings which have to be done at the shoulder.)
Lengthening the sleeves is more iffy. As EzraPaul notes, lengthening them slightly is often possible (and simple). I can't say whether the sleeves on the jacket in the picture can be lengthened adequately for you. If so, great. If not, don't buy. Simple as that.
And for Dog's sake, take breakaway01's advice and tuck in your shirt. You say you want to start dressing like a man. Well, that's good. That's a fine goal. And a man knows when to wear his shirt untucked, and when not to. When trying on suits - and taking photos of yourself in the suit to share on SF for comments on fit, no less - is definitely one of those times when the shirt needs to be tucked into your pants.