The size difference between DSLRs and mirrorless is only because:
(a) The lack of the mirror box. This has no effect on telephoto lenses though. They will simply have to be longer.
(b) Wide angle lenses can be more compact, if the company in question knows how to make sensors that can handle the steep angles of light (usually digital sensors want the light falling quite straight onto them). Only Leica has really managed this with their digital M. The Sony A7s is maybe even better than the Leica M, able to handle lenses the M fails, but the Sony A7, A7r and A7mk2 have trouble to adapt wide angle Leica M glas. While any DSLR glas can be adapted easily because by very principle it doesnt have this issue.
(c) Other than that, mirrorless system cameras are only smaller because the sensor is smaller, and because the maximum aperture of lenses is smaller. The Sony A7* cameras use a full frame sensor. While there are quite compact lenses for it, such as the 35mm f2.8 or the 55mm f1.8, in general lenses arent smaller and the whole package is hardly smaller than a DSLR.
About what mirrorless system to pick, you kind of demanded a general intro:
- Mico Four Thirds have a rather small-ish sensor (17.3x13mm) and a very broad lens lineup with many quite good offers. The cameras are sold by Olympus and Panasonic. There are very high quality offers around, probably the best mirrorless cameras right now. Both Olympus and Pansonic have a pretty complete offer for lenses, so you can cherry pick which you want. Panasonic has developed an advanced type of contrast autofocus which analyzes the unsharp areas of the picture to more effectively drive lenses; this makes this system theoretically especially performant with sports, though in practice the differences are not that feelable.
- Fuji X is APS-C (24x16mm) and has very high quality glas offered. Theres also some glas from Zeiss for it; all Zeiss Glas is also offered for Sony E.
- Sony E, another APS-C offer, is a bit on the backseat now that Sony has come out with the full frame version.
- Samsung NX is also APS-C. Only Samsung provides camera bodies and lenses right now. Its innovative in some areas (WiFi, 4K Video, IIRC also phone integration ?).
- Canon EOS-M is the unloved stepchild of the Canon EOS DSLRs. This system has an overwhelming array of 4 native lenses and is infamous for its rather slow autofocus. A shame, really, considering Canon developed the Dualpixel Technology, which would allow good sport autofocus even in low light, like a DSLR can do. The image quality is good though and the system is really very compact.
- Sony FE, the full frame (36x24mm) version of Sony E, is relatively new, but already has quite a number of lenses out. Especially the prime lenses are of very high quality. This system is definitely NOT small unless you limit yourself to selected lenses (like the aforementioned 35mm f2.8 or 55mm f1.8).
- I'll ignore Nikon 1 and Pentax Q due to them being very niche products with very small sensors.