Personally I prefer Altoholic. You can see and search bags, banks and guild banks across all you characters, but also Altoholic does so many amazing things for multiple characters as well.
For each character you can also see what currencies, bag slots remaining, gear they have, their talent build, if they have mail and how long until it expires, what recipes they have, their reputations... With 10 alts, I couldn't live without it at this point.
You can find detailed information on available mounts at WoWpedia. I'm not going to list all available mounts here, but you can find them all at that page. I'll try to summarize the general approaches you can take to getting a more exciting epic flying mount.
Basic wyverns are available from vendors when you hit level 70 and buy the Artisan (300) flying skill. Other mounts like the various drakes are typically available as faction mounts or rare drops.
Some are boss drops such as the Bronze Drake, others are reputation rewards such as the Netherwing Drake Mounts or the Red Drake. If you're a tailor, you can craft a flying carpet or its winterized version. Engineers and alchemists can also create flying mounts for themselves.
You can also buy this blue wind rider from Dalaran, but it's not terribly different from the common mounts except in colour.
Last but not least, there are mounts like the Violet Proto-drake that are awarded for getting certain achievements.
As you can see, the list of options is long and varied. Since you're nearing level 85, pretty much any of these should be available to you at least as far as plain level requirements go. Which mount you should go for first depends entirely on what you feel like getting and how much time/gold you're prepared to spend to do it.
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There are two different types of pets: class pets and companion pets. The former you only get if you're a certain class: warlocks get demonic minions, hunters can train animals to be pets, death knights can get undead pets, and frost mages can get a water elemental as a pet.
But I have a feeling you're talking about so-called companion pets. Companion pets are rewards for all sorts of things: achievements, quests, out-of-game events; some are even available for purchase with real money.
The best way to find out how to get one is to figure out the companion you'd like to have first, and find out what you need to do to get it. To that end, the website WarcraftPets.com has a searchable database that gives all the details about the different companion pets.