Don't focus on sets, focus on stats. Unless you really need a certain effect on a specific champ (lifesteal for CB/dungeons if you don't have healers, shield set on a high HP champion, freeze set on a AOE provoke champion, would be some examples), your first priority is getting the right main stats and substats on your champion - set bonuses are something that comes on top, if you're lucky. Far better to miss out on a third set bonus but have good stats, than to get that third set bonus but with a weak item. 

Ignore the reviews button. Ignore Ayumi's set recommendations - or okay, not quite ignore, but they are much, much less important than his main stat recommendations and general stat priority advice for each champion. 

And no, there isn't a cheap or easy way to switch between different gear combinations for arena or dungeons. Same thing for masteries. In the beginning, you'll just have to compromise - on champions who you use in arena as well as dungeons/CB, you'll usually want to give dungeons/CB the priority. Once you get further in the game and can start specializing more, you'll develop arena-focused champs with gear and masteries tailored to arena. 

Thanks for the comprehensive answer! Only level 35, so yeah I'm some distance from tailoring different champion sets.

One further question, though, resulting from your response: is there somewhere a list of main stat recommendations for champions, or is it in the game somewhere I haven't found yet? Obviously attack/support/defense is a good bellweather of what's targeted, but is there something more detailed available?

Thanks again for the advice.

Ayumilove has that, right underneath his set recommendations that you referred to. 

Of course main stats are always the same for weapon/helmet/shield, so you only need to consider it for gloves, chest and boots, as well as the accessories (ring/amulet/banner) but in early game, you rarely have much choice on the accessories so you take what you can get for that faction. 

Boots are the easiest because you almost always want speed main stat - of course that won't be possible in the early game, so put your good speed boots on your highest priority champions and try to get at least a speed substat for the others. 

Chests are usually either attack percentage for offensive champs, or hp/def percentage for support. Maybe accuracy on debuffers, until you can get an accuracy banner for them. 

Gloves are crit rate or crit damage for offensive champs, hp/def percentage for support or for champions whose damage is based on defense. Attack percentage only in rare cases. 

On all three, the 'flat' attack/defense/HP gear is really bad - only consider it if the substats are exceptionally good or you really have no other choice. 

Yeah - basically, flat ATK/DEF/HP on gloves/chest/boot is auto-sell. ATK % on DEF-based sets for chest is auto-sell.

Gloves, usually you want crit dam if you can get crit rate from other items. The basic equality formula is Crit% * CritDam% + 1 - IE, for example, if you have 75% crit rate and 100% crit dam, your effective bonus is (0.75 * 1) + 1 = 1.75. That would be equal to 100% crit rate and 75% crit dam (of course), as well as 50% crit rate and 250% crit dam.

Chest, ATK% for ATK champs, DEF% for DEF champs, etc...

For weapon/helm/shield, base it on the set and the substats.

That all makes sense, and tallies with what I've read. You both clarified things well, much better than those YouTube videos with cats wailing in the background.

Thanks to both of you for taking the time. It's much appreciated (and duly bookmarked!).