What is the easiest way to level up my profile?

If you're looking for games with as little cards as possible, the following incomplete list shows games which only have five cards each:

• Don't Starve
• Super Meat Boy
• The Swapper
• DLC Quest
• Trine 2
• Bastion
• The Walking Dead
• Bleed
• Counter-Strike: Global Offensive
• Defy Gravity

for a probably complete list of games with trading cards, have a look at this one

Costs: With a current card price of ~.2$ per card, that's about 1$/badge, so 100XP for 1$. Due to the level limit you cannot do this forever with the same game though

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Other ways to obtain XP are:

• "Years of service" I got 250 XP for five years, so I guess it's 50 XP per year. Costs: time
• "Community leader" (Max: Lvl 3) Just do 28/29 of the stuff mentioned there (post a screenshot, trade, link to facebooke etc). Costs: Data
• "Director of Acquisitions" some XP per game you own (1-5 XP/game, see here as per Nolonar's answer). I don't know how DLCs count here, and the scaling is probably non-linear. Costs: a lot - even with an optimistic 10$/game you have to spend about 1000$ for another 100XP once you have many games
• "Steam Summer/Holiday Sale 201X; Potato Sack; Trading Card Beta Tester": XP based on the achievements/participation. Costs: A time machine...

So in summary, apart from the up to 200 XP from the "Pillar of community" badges the most promising source of XP are indeed gamecard badges. The badges with fewer gamecards are probably easier to obtain, but then again they may also be more expensive on the market.

By far the easiest way, is to do nothing.
You get 50 XP per year since your registration.

By far the fastest way, is to buy games with trading cards as well as their cards.
For every game owned, you get a few extra XP; For more information on how many games award how much XP, read here. Trading card badges awards 100 XP each. You can only gather half of the cards available per game, unless you receive a booster pack. For the rest, you have to trade.

This is my little strategy to farm some XP and Boosters.

-Buy low priced games from Bundles and sales. Like Humble Bundle (~5 games for 1$ minimum). Look up if there are any games with trading cards first, in case you're not interested in the games themselves.

-Look for games that needs like only 5 cards to make a badge. That way you don't need to put much money into buying the cards that are left. And you can also sell your other cards for games that need like 15 cards to make a badge. In that way you will level pretty fast.

-Get eligible for as many games you can for a higher chance to get booster packs. I'm currently eligible for ~25 games and I have maybe ~50 trading card games left to farm.

-Buying games from bundles etc is a good, cheap and pretty fast way to lvl up since you get xp for every game you buy/own. And if you love playing games like me it's another bonus for you!