Tim,
Sure there are a lot of guys who do not go all primitive. In fact, I'd say carbon arrows are almost more common that woods anymore. At least you see a lot more questions about them. As for flipper rests, nor sure which type you mean. There is a stick on sideplate/rest that has a little black plastic shark fin kinda rest that some guys use but I'd say probably 99% shoot directly off the shelf. The general idea is to get the arrow as close down to your hand as possible to help shooting instinctively. It's just a more natural "point and shoot" thing. Even if you are gap shooting or using some sort of aiming method, it still helps you develop a better feel for the shot.
As for arrows, you can buy pre-built arrows in either cedar or carbon but you still have to buy broadheads. Most of the time if you buy a dozen cedars from a vendor, they will cut them to length and put target points on them for you.
One word on broadheads too. Stay away from the mechanicals and modular types common with compound shooters and go with either a two or three bladed cut on contact head. They out penetrate the others by a BUNCH.
If you already have arrows left over from your compound, you could probably have the vanes replaced with feathers and shoot them if the spine is correct.
Have you had your draw length checked yet? Most guys seem to loose an inch or so going to a corner of the mouth anchor, fingers shooting traditional style.
Search also for O. L. Adcock's arrow tuning page. He's got a good explanation of the whole arrow tuning process. Really more info than you need but a great source.
If you know nothing about spine, here's the short version.... There are two categories of spine. Static and dynamic.
Static spine: What arrow makers use. An arrow shaft gets placed on two supports 26" apart, hang a two pound weight in the middle and measure the sag (deflection) in thousandths of an inch then convert with available spine charts to determine bow weight range the arrow will work in. If testing wood arrows, grain orientation makes a difference. Test with edge grain going up and down.
Dynamic spine: How the arrow acts while being shot. Trad bows are usually not quite center shot so the arrow has to bend around the riser when you shoot. Dynamic spine is just that. It is a moving "dynamic" flexing of the arrow when yo shoot. Because it is dynamic, multiple factors effect it. That's where I was talking about arrow length and heavier or lighter points above. Other factors are the actual power or performance level of the bow, string material, string weight and the shooters form.
Most guys bare shaft their arrows to tune them to their bow. If you are right handed, a stiff arrow will fly tail right and a weak one tail left. However, point of impact is equally important and O.L's site explains all that.
For actually tuning your bow, the two main things are to adjust the brace height (distance from the string to the lowest point on the handle) and adjust your string nock position. Usually it is around 1/2" above the shelf give or take 1/8" but sometimes close to 3/4".