I need some help on which type camera to buy.

The difference between a DSLR (or Digital Lens Reflex Camera) vs. MILC (or Mirrorless Interchangeable Lens Camera) camera is the way it displays the subject you're preparing to shoot. A DSLR is just like the old 35mm SLR cameras, which I'm going to bet you've used in the past. The subject is seen through the viewfinder by capturing the image coming directly thru the lens where it's deflected upwards (and outwards) to the viewfinder via a mirror. When you press the shutter the mirror flips up and out of the way to allow the light to come thru the lens and hit the sensor (for digital) or film (for 35mm).

A MILC does not use a mirror, hence the "mirrorless" designation. It shows you the subject that you're about to capture via a small display screen in the back of the camera that is captured thru the lens of the camera. Some of them also display the image via an EVF (Electronic Viewfinder). This might be one of the points of sale here, because for me, unless the MILC has an EVF I wouldn't touch it at all. Seeing your subject via a small screen in the back is not the best way to see it. Often times lighting will make it near impossible to see much of anything.

About the only areas where I have seen that MILC would be better than a DSLR is in burst mode shooting (shooting multiple images in very fast succession), since there's no mirror to flip up (that takes time) they can shoot faster bursts. The only other area would be in shooting video, but then again why are you using a still camera to shoot video?

I prefer the DSLR because I'm not a young guy either and I've had plenty of experience with the old SLR cameras, so it's familiar territory. The MILC's are a BIT light in weight than a DSLR, but most DSLR's complete with lens are around 1-1/4 pounds (hardly a heavy load).

The DSLR is going to give you access to a LOT more lens and accessories, whereas the MILC's do not have as many options and for some of the proprietary models the selection is basic at best. Since you mentioned wanting a telephoto lens, then I'd definitely go with a DSLR. They might be just a bit more bulky, but they've got a lot more options AND should be very familiar to you.