There really is no sure way to 100% ensure there will be no mess. As to suggestions on how to lessen the odds, I would say first off make sure you are getting enough fiber in your diet. Also make sure that you empty your bowels before but it doesn't have to be right before. As one of my guy friends always says "Know your pooping schedule."
Since there is no way to actually guarantee mess free time it doesn't hurt to keep wipes on hand. Regular baby wipes are fine and can easily be stored. Also condoms are really not a bad idea. Even if the relationship is monogamous and both parties are healthy it can help make clean up easier should there be a mess. Another added bonus is the male can remove it and switch to vaginal penetration if the partner has any discomfort and wants to stop the anal activity. No need to wash up, just remove and replace or remove and insert.

I have never suffered from fecal incontinence and I have engaged in a lot of anal play over the years. I have had plugs, beads, fingers, probes, dildos and dicks all up there, including the use of beads inserted "beside" a dick for both our pleasures.

As to your other questions. I would start with smaller beads and gradually work your way up. I can't really offer you any suggestions here I am sorry.
Besides the ones you listed But you might want to check these ones out:

Posh Silicone Beads
Silicone Beads

Butt Plugs on the other hand I have multiple suggestions for.
It is out of stock but Beginner Anal Kit is a great set. Mood Naughty is also a great line. Different shaped plugs in different sizes. Candy Rimmer Seems be a smaller plug also.

You can also explore with both beads and plugs. Try both, there is no set standard for what comes first. You might actually find it easier to start with a plug first and work your way up to beads or the opposite might be true.

Lube wise my only suggestion is make sure that it is Glycerin free.Glycerin is the main ingredient in suppositories used to fix constipation. This could cause some issues as you can imagine. I have found that silicone lubes work better for anal sex, but I use either a hybrid or a water based gel for use with my silicone toys.
I enjoy Wicked Jelle myself for use with my toys. The lube that you mentioned seems to be Glycerin free so that is a good thing and should be fine to use for anal play. You might have to use a little more than usual depending of its slickness and lasting power.