You can use your Mr. Beer fermenter to do 2 gallon batches. You can lookup any of Northern Brewer's recipe kits and under "details" there is a link to the PDF instructions which include an ingredient list.
The recipes are meant for 5 gallon batches so just multiply all the ingredients by 0.40 and you will get the amount needed for a 2 gallon batch.
Most of the recipe kits use light LME and steeping grains to build the malt base of a wort. There are usually 60, 30, and 5 minute hop additions but some styles only use a single 60 minute addition while others may also dry hop.
Keep in mind the yeast can also impart a lot of flavor to your beer. Using Safale 05 vs 04 for instance will give you very different beers even if the malt & hops are identical.
I personally don't even use steeping grains. My LBS has "kegs" of light, amber, and dark LME. I'll just combine them to get what I'm looking for. I also try to keep things simple and use a single hop variety.
My philosophy is that it's pretty had to find ingredients that make a "bad beer" if you are just using malt extract and hops. If you're adding in a bunch of other stuff you can create some pretty funky flavors, but with malt extract and hops you are pretty safe. The challenge of making a good beer is maintaining proper fermentation conditions, keeping the yeast happy, and preventing infections & oxidation. This basically comes down to using the best practices for the equipment you have, keeping an eye on the beer, and taking good notes.
The main points I would emphasize are.
*Keep a bucket of sanstar handy while you're brewing - when in doubt sanstar, don't be afraid of putting your beer on the sanstar foam (also if you keep it in a sealed container you can reuse it)
*Cool your wort as rapidly as you can, I put my boiling kettle in a cold water bath and keep a small amount of cold water running. This gets ~2.5 gallons of boiling liquid to ~70F in 35 minutes if I use an ice bath to start it out.
*Don't pitch your wort until it's cooled down to under 70F
*If you are fermenting where the air temperature is over 65F put your carboy in a plastic storage bin and use a water bath to keep temperatures cool & stable. If things start to get too warm I throw a frozen 20oz bottle of water in the water bath which drops the temperature 1-2F after 30 minutes. This step isn't possible with a Mr. Beer fermenter because they have small holes in them to release CO2.
*Once things get going leave your beer alone. Only open it up to draw a hydrometer sample. Try to give it at least 2 weeks. 3 weeks is preferable but the Mr. Beer fermenter is not air tight so I would go with 2 weeks until you get a carboy or bucket.
*Invest in a bottling bucket, it is much easier than trying to hand prime each bottle.
*Give your bottles at least 2 weeks in a warm place, if your house is closer to 65F expect to wait 4+ weeks for the bottles to properly carb.