It's only ever necessary to carry 2 of each Power Gear at a time. Pokemon can only have up to 2 slots for Power Gears(this may change in the future.)
Keeping two of each type of Power Gear leveled up as much as possible is all that's needed. All other Gears should be transferred for Upgrade Kits.
Summon Gears can and likely will only be able to be equipped one at a time. It's never necessary to have two of a Summon Gear at a time. Transfer them for Upgrade Kits when you can.
Ore Management and Tickets
You have at least 3 slots for refining Ore at any time. If you receive an Ore from an Adventure while you have 3 Ore queued up, you must delete an Ore you aren't refining. You can only delete 10 Ores from your queue in any given day. Discarding Ore that was just earned is unlimited.
Also, please note that you can only hold a maximum of 10 Tickets at a time. You receive 3 Tickets daily as part of a log-in bonus, so when you log off, make sure to have at most 7 Tickets in your inventory at a time.
Finding the Right Adventure
Looking for the right Pokemon on the map is very difficult. You are able to see a collection of other player's adventures, but clicking the right pixel is tough unless you're using a stylus or other device. There are two ways to be 100% certain of what Pokemon you will be fighting.
Recent Adventure List
In the bottom left corner of the Adventure screen, there is a list of the last 3 maps you have visited. You can even "lock" one of the maps in so that it won't leave the list when you pick new stages.
From the main menu, select "Menu" in the top right corner and then "Adventurers".
The Adventurers List will allow you to select from a list of players who have recently used your spawn point. You'll be able to play any level they've recently completed! These levels won't show up on your recent list though.