First off, congratulations on entering the world of robotics. I hope you enjoy it as much as I have. You are correct that the L298N has a voltage drop that is between 1.8V and 3.2V (at 1 Amp) or 4.9V (at 2A). This is a problem I sometimes see in older generations of H-bridge designs. After you figure this problem out and move on, I'd recommend switching to something a little newer like the TB6612FNG or maybe the DRV8871, both of which are pretty common, smaller, and more efficient. But that's a future step. First lets get this current project powered.
I'm having to make some assumptions based on the images that you linked to but I'm going to assume that the motor board can take up to 12V and that it ouputs 5V that you are using to power the arduino. I'm also going to assume that those yellow motors are the familiar cheap hobby motors that run at 3-6V. If any of those are not true, please comment and we can see how things change.
Now as to what kind of batteries to use; there are literally thosands of ways to power this. One option is AA batteries as you are doing now. I would use maybe 6-7 AA batteries to account for the voltage drop of the hbridge but remember that they start at 1.5 but can quickly drop voltage. And the more current you pull from them, the faster they will drop. This will be cheaper if you only want to run it a few times since AA batteries are like $0.50 a piece in bulk. But if you want to run it a lot to experiment, it's going to get expensive (and annoying) fast. Another option is to use NiCad or NiMH batteries that are rechargable. The batteries will be a little more expensive initially and you'll have to buy a seperate charger but this will save money in the long run and be able to supply more current to your motors. NiCad and NiMH batteries are 1.2V (nominal) but come packaged in battery packs so I'd recommend probably an 8.4V pack. Finally there is the Lipo battery packs, also called Li-Ion (which is a much better and more accurate name but I won't get started on that). Li-Ion are rechargable like NiCad and NiMH but are much smaller and lighter for the same energy capacity (mAh). Because of this they have become very popular and have become pretty economical. For instance you can get a decent li-ion for under $20 on hobbyking and be very happy for several years. Li-ion do have an inherant risk but as long as you don't do anything stupid, you'll be fine. They also require a special charger but as long as you aren't worried about super fast charging this isn't too expensive. Li-ion come in individual cells of 3.6V nominal (sometimes advertised as 3.7V) but also come in packs of 7.2V, 11.1V, or 14.4V. Remember that these are the nominal values. A 7.2V pack will start at 8.4V and drain to 6V before it is "dead" If you go this route, I'd go with the 7.2V pack.
I would highly recommend you go with one of the three rechargable options since that will be more economical in the long term and will also allow for longer run times and will supply more current to the motors. Hobbyking.com is a great resource for cheap rechargable batteries as is amazon.
I can't explain everything but here are some further quesitons you should google to get started:
-Lipo C rating
-Lipo voltage range
-Lipo mAh rating
I just want to fix a couple misconceptions from other answers:
1) Lipos are not expensive as hell if you take into acount how long they last and their other benefits such as size, weight, and ability to supply current.
2) For a given battery capacity, a LiPo will be smaller and ligher than AA batteries and will provide more current and longer battery life than AA batteries. The ammount of current the Arduino draws will be tiny compared to the current of the motors so don't worry much about it.
3) Not only are Lipos recommended by many people for ground (and air and water) robots, they are becoming the standard for RC cars of almost every size. The motors you are using here are 6V max so 7.2V lipo is a good way to go. Later you might use motors that are 12V and will move up to a 11.1V or 14.4V lipo. Some of the nicer lipos can deliver hundreds of amps to motors and are commonly use in battlebots and similar competions. But you aren't there yet so you're going to use smaller lipos with these smaller motors and maybe someday you'll use big lipos with big motors. Every project has different needs.
4) Sometimes a rechargable battery back will get hot if you are pulling a lot of curernt from it. But as long as you respect the "C" rating (google it) you will be absolutely fine.