I switched to cups in 2010, at the age of 20. It was no big deal, actually. I soon found out that many of my friends were still using pads (I somehow assumed that everyone else uses tampons). I also found out that it's absolutely not uncommon to switch directly from pads to cups.
In fact, tampon users have to unlearn some habits when switching. Specifically, cups don't need to be inserted as deep as possible, and they're generally a little more hands-on. You can't really just shove them "up the black hole", which is why all the attempts to create a cup with an applicator haven't had much/any success. Honestly, cuppers generally agree that applicator is not needed for cups. It's likely to do more harm than good. (This doesn't mean that those who use applicator tampons can't use cups)
Also, cups have to be aimed towards the tailbone/rectum. Getting the angle right is more important with cups.
On the other hand, if you happen to insert it incorrectly, removing and reinserting is no big deal. A major benefit of cups is that you don't "waste" the capacity if you remove a cup that isn't full. In fact, one of the best tricks for removal without spilling is to remove a cup when it's 50-75% full (especially as a newbie).
Besides, not everyone can use tampons. The companies tend to pretend it's all user error, but the truth is that they cater poorly to some kinds of anatomical variation, especially a low cervix. If tampons are too long/slide down/get saturated only in the bottom half, your cervix is probably low. In this case, you should avoid the DivaCup and some other long cups, but there are plenty of options. (If you already have a cup that is too long, flip it inside out to shorten it)
For pad users (like I used to be), the biggest challenge is learning to insert something that is not your own finger. In the beginning you may need a mirror. (If you're not very familiar with your anatomy, see the virgin's guide to cups, even if you're not a virgin)
If you like the eco-friendly aspect of cups, you can also consider cloth pads.
Remember that people prefer pads for various reasons. Some always leak with tampons, some can't afford to buy tampons every month, others are concerned about the toxic shock syndrome. (There are no documented cases of cup-related TSS!) Some are indeed squeamish about the idea of internal protection, but it may well be a smaller percentage than you assume, or specific to internal absorbent products. Your friends who use pads can totally like the idea of a cup, or spread the word even if they don't want to use cups themselves! Don't limit your cup conversations to those that use tampons. And mention cloth pads along with cups.
Furthermore, it's a big marketing point that cups can be used for up to 12 hours (and the off-label longer usage is not uncommon). The real point here is that it's safe to wear them for a long time, but nobody can guarantee that a cup won't overflow earlier, especially the low or average capacity brands like the Diva, Mooncup UK, Keeper/Moon Cup US, LadyCup.
Nevertheless, prior to using cups many used to think their flow is much heavier than it is. And cups are better at coping with a gush of blood, or with clots. Most cups have a higher capacity than even ultra tampons (see the size charts), and several brands hold twice as much as super plus ones. I know a woman who used to change super tampons every hour, and can go 6-10 hours with a cup now! (Not everyone is that lucky, of course.)
Similarly, if you change pads a lot, think of why you need to do that. Do they get full, or are they just uncomfortable after a few hours? Are you avoiding the highest absorbency pads due to their size, preferring to change normal pads more often instead? Or are you perhaps using overnight pads for their length, despite not needing the absorbency?
These questions should help you figure out how heavy your flow really is. There's also a scale for that, based on pad/tampon use. When in doubt, go for a higher capacity cup.
(See also: An overview of the highest capacity cups)
The bottom line is that everyone's journey is unique. Apart from being able to insert 1-2 fingers into your vagina, there are no requirements for using cups. There's no need for a "transitional" method, like applicator-free tampons or Instead SoftCups. Nowadays new users are increasingly likely to get a cheap cup from e-Bay before making a more significant investment - if you do that, be sure to choose by the dimensions anyway, and bear in mind that they can have a lower quality, be too soft etc. Consider trying out a relatively cheap cup like the Fleurcup, Meluna, CupLee or Yuuki instead.
Just remember that you can always go back. In the beginning most cuppers use cloth or disposable pads for backup, and going through the learning curve may take a few cycles. Start by reinserting the cup as often as you'd change absorbent products, and soon you'll see how long you can go without emptying. Allow yourself to alternate cups with disposables or cloth pads if needed.