I sleeved RotR with MayDay sleeves -- 66x91 that come in 80 count packs. This was a bad choice. Maybe some MayDay sleeves are better quality, but these fell apart frequently. I had to resleeve a number of cards while playing through the set 3 times.
Since then I've used Ultra Pro Deck Protectors. I thought the hologram (which I still think is ridiculous) would bug me, but I never notice it, honestly. The quality is much better than the MayDay. I find 1000 or so for sale on eBay and buy at a decent price.
I wouldn't use penny sleeves, I think they're way too flimsy.
I use Dragon Shields for the double-sided cards. You can't beat Dragon Shields for quality, but they're wicked expensive. There are only a few double-sided cards, so it's not too bad.
I use the Broken Token box organizer. I had some problems with the RotR one -- the columns widen and the dividers fall out -- but for some reason since then there has been less of that problem. Go7gaming has one as well. Other people have rolled their own, if you check this forum and boardgamegeek you can see examples.
I use Ultra Pro inner fit sleeves for the double sided cards (they're snug but they still fit, and I can write on the sleeves with sharpie to check off feat boxes) and Dragon Shields for the normal cards because they shuffle really nicely and are quite durable. I would not recommend penny sleeves for deck cards (double sided is more ok), you'll go through them like crazy as the sleeves get bent/wrinkled (thus identifying the card) and they're a pain to shuffle.
I use the included insert, but I need to be creative in order to get all the cards to fit in. Often I'll use the unused character deck slots as overflow for the boons which don't all fit in their respective slots.
I use Ultra Pro Clear Standard Sleeves, with the holographic dot on the back (so it doesn't block any text). I've also received quite a few of these sleeves that don't have the holographic dot, so these are used for the double-sided cards (locations, characters, etc.).
I use the PACG Organizer from the Broken Token for all of my sets. The previous version of the organizer had some problems, as previously described, but I've found that simply replacing some of the dividers with the new dividers solves the problems.
I've found that all of the cards for the AP (base set, character add-on deck, all adventures), all of the promo cards, plus all of the OP "Season of" cards fit in the box when I use the PACG Organizer (it's heavy, but it's worth it).
I use the same sleeves for all of my class decks and I store each fully-sleeved class deck in a 300-card box. They can all fit in a 200-card box, but I store them with dividers, which don't fit in the box unless they are stored sideways.
In preparation for OP, I have decorated sleeves so that my cards can be distinguished from other players' cards (which really only matters if someone else is using the same class deck). For me, I have the Flying Monkeys sleeves from Ultra Pro; and my wife has the Dia de Los Muertos Pink Skull sleeves, also from Ultra Pro. If we ever play in OP, we would have to remove the cards from their current clear sleeves and put them in the decorated sleeves. I'm much more likely to shuffle a class deck or two into the box for regular play, though, so I keep them in the clear sleeves.
The Penny Sleeves can be problematic (at least in my opinion) because they are much taller than the cards. While the "nicer" sleeves are more expensive, they really are worth it. But you have a few options:
1. You don't need to sleeve every card. This is the most economical approach you can take. Just sleeve cards that are in your character deck and as you add them to locations or the blessings deck. It is more work, but you use less cards. A hybrid of this and sleeving everything is to at least not sleeve the henchmen or villains.
2. Sleeve everything, buy in bulk. Various sites offer quantities of sleeves in the range of 1000. The bigger the quantity, the cheaper "per sleeve" price.
3. You can get a nice insert, like the Broken Token one (which I use) but you can also go economical here. Get corrugated cardboard boxes, designed for cards. Often advertised for baseball cards or magic, a few of them can fit in the Base Set box and store all your cards. Calthaer recommends a 660 count and 2 550 counts.
Lastly, as a side note, it seems that more recently produced Ultra Pro sleeves have dropped the use of the hologram. There are still loads of older ones for sale out there, but if you are in a store looking at them, look closely to see if they have the hologram or not, if that matters.
For most sleeving needs I use KMC W Version, which are KMC's clear glossy sleeves. If I double I also use KMC Perfect Sizes for the inside.
Penny sleeves tend to be loose on cards and easier to wreck. They're fine for non-game cards that you aren't shuffling and manipulating all the time.
I use a Broken Token insert for box organization and various larger deck boxes (plastic ones designed for 100+ cards) for Guild play class decks.