How far you choose to take your achievement hunt is up to you, of course. Personally, I am fixing to be quite the achievement junkie. Still, not all of them will take time, effort, fat wallets and endless patience to acquire. In fact, there are some achievements up for grabs that require such little effort that you might as well snatch them up.
Can I keep him? Obtain a vanity pet. Seriously, all you need to do is hop over to your local vanity pet vendor, or the auction house, and pick one out. If you already have one, great. Click on the item to "learn" it, as the items are now considered spells (as are mounts).
It's Happy Hour Somewhere. Drink 25 diferent types of beverages. This will require a bit of traveling, but it's definitely a fun one. Start with all of the main waters, from Refreshing Spring Water up to Purified Draenic Water. Then seek out the coffee vendor that walks the path in Lower City, and you should be up to ten. Bubbling Water and Enchanted Water, both easy drops, will bump you up to twelve. Check out the vendor outside of Shadow Labyrinth or in the Stormspire to collect another two water. The Bar Maiden in Shattrath has five alcohols, bringing you to a total of 19 drinks. If you're tired at this point of checking every bar and Innkeeper around, start visiting your faction reputation vendors. Usually after friendly, good eats and drinks are offered.
Represent. Collect one out of the 47 tabards. If you aren't in any position to grab one of the Outland tabards, try running the Scarlet Monastery - Armory until the Tabard of the Scarlet Crusade drops from the mobs summoned once you've downed Herod. This makes a leisurely guild project, and gives you a chance to goof around on Vent; because you know, no one ever does that during serious raiding.
Duel-icious. All you have to do is simply win one duel against another player. This one is so easy, you can rig it.
5 Daily Quests Complete. Finish five daily quests. This one is too easy, as long as you are level 70 and eligible for most of the dailies. Even if you hate the daily quests, there are some for everyone. From the gathering quests to the daily battleground, cooking and fishing quests, I'm sure you can drag yourself through five.
Update: Someone in the comments asked about titles -- the easiest title to get is probably "[Name] Jenkins." You can nab that one just by killing 50 rookery whelps in 15 seconds, so grab some AoE, run to UBRS, and spawn kill whelps as fast as you possibly can.
Other than that, they're relatively hard. Earning Exalted with the Cenarion Circle and the Cenarion Expedition will grant you a title, so if you've got one of those, you could just work towards the other to pick up "Guardian of Cenarius."
Doing 3000 quests will get you "The Seeker," so if you're close there, you could turn in a bunch of low level quests and see if you can hit that number quickly. Other than that, the title achievements are pretty complicated (and/or require Northrend to be opened up, which it isn't yet, obviously). But hey, you could always spend that 1000g for "of the Shattered Sun," right?