You can obtain several Power armors in the game, some may might be complete set and the other may be missing some parts. Since you can't transport them, you have to power them up first by installing a Fusion Core before you can equip them. While you have them, you can just fast-travel to your main hideout where you can safely leave it. You cannot lose your Power Armors since their locations will be permanently revealed in the map.
The type of Power Armor you'll find in the map will depend on your level. Since you can get a complete set in the second story mission, don't exert extra effort looking for the other armors until your level is at least 28 so you'll still have a chance to find better quality Power Armors. This guide has a guide of all Power Armor locations.
As an additional note, if you're leaving your Power armors in a location with other NPCs (caravan guard, settlers, provisioners, quest NPCs like Brotherhood Scribes, etc) are around, make sure to remove the Fusion Cores or these settlers will equip them and use them to fight off the invaders. When used by NPCs, the fusion core energy will not be spent. However, the Power Armor itself will take damage and you'll still have to have those parts repaired. If a part is missing from the power armor, trade with the settler to retrieve it.
If ever your Power Armor has been equipped by a settler, you have to wait for things to calm down before you can ask him or her to get out of the power armor. This may take a few days (in-game time). You'll know if the situation's back to normal when they don't have a looping conversation option and your shops have resumed bartering with you. If your power armor is worn by non-settler NPC like caravan guards or quest NPCs (like the Brotherhood of Steel scribes), you won't have any way of forcing them out of it, unless you kill them and forcibly eject their fusion core to disable the armor.
Power Armors can also be modified and upgraded. However, high-tech upgrades like adding an integrated Tesla field, jet boost, auto-Stimpak, integrated Stealth Boy etc require high Science perks so don't bother tinkering with your mechanized armor too much early on. Power Armors can be modified at any Power Armor station.
If you remove all parts of a Power Armor, what's going to be left is the Frame. The frame itself still requires a Fusion Core attached in order to be used. And surprisingly, even without a helmet on, the hud will change like a normal power armor interface on. Frames doesn't offer that much protection or provide extra abilities or stat bonuses but they'll still negate fall damage and will still significantly boost your capacity to carry loot around.
Some shopkeepers can also sell Power Armor Frames. Rowdy in the Atom Cats Garage is probably one of the earliest shops you can access selling power armor frames, parts, and mods.