From listening to the podcast, at first I thought a longbow would be good, then a guy up where I camp says they are hard to pull at 60 pounds or so and instinctive shooting takes years to learn. I'm not sure which way to go ..
My mother doesn't want me target practicing in the back yard, I'd have to go out in thee woods with one of those little hard foam box targets
For the sake of disclosure, I shoot a longbow, so you can assume I am biased to some degree.

But having said that, instinctive shooting is all about hand eye coordination. If you've spent any time playing video games then your brain is already trained (to some degree). I'm 36 & while many of my contemporaries are video game players, I never was, so it's taken me a bit longer probably to be comfortable with no sights. It doesn't take years, not for most people. It just takes consistent practice.
It takes regular practice to shoot a bow without sights, but there are sighting options available for even longbows & recurves. In fact, you can make your own sight with something as simple as a matchstick & some electrical tape. You only have to be willing to experiment a little to find proper placement on the riser in comparison with the average yardage you want to be able to hit proficiently. I linked a couple of archery sights
Here. If you think you're interested in trad archery I can help you get set up pretty cheap. You can definitely become proficient quicker if you wanted to go the compound route but I've not shot one in a long time.
You don't need a 60 pound bow to take large game. In fact, I hunt with a bow that's only 45#'s & it's plenty capable of taking deer sized game. There used to be a trend toward "heavier is best", but it's just not the case. Starting out you should shoot something that's comfortable for you to pull consistently because getting the proper form is the most important aspect of shooting any type of bow. If you're interested in learning more shoot me an IM & I'll be more than happy to help or answer any questions you may have.
Shane