The best way to burn through your fat is a cycle of HIIT. HIIT is High Intensity Interval Training. What this means is that you do a particular exercise for a short period of time in which you bump your heart rate up very high (depending on your age it varies from 180 - 200 bpm).

The benefits of HIIT are, you're done quickly, you will be burning fat for up to two hours post training and it makes you feel like a beast when your done.

HIIT exercises I would suggest:
- Death by Burpees. Here's a video: (edit I can't post video's yet because I'm a new user, please just google Death by Burpees and click the 1st video)
You basically start of doing one burpee in your first minute. Then you do two in your second minuten, three in your third, etc. You do this till you are completely exhausted. Not out of breath, but literally feel like dying.
- Bag combo + squat + push up + 5 situps. This is basically when you do a simple combo on the bag, for example, left straight, right straight, left hook, right low kick (you can find many basic combo's on youtube). You then do a squat, then a push up followed by five sit ups.

You can also make up your own exercises. As long as it raises your heart rate up to close to it's potential max.

As for Paleo, Paleo is basically when you eat as a Paleolithic man (pre-historic). You simply eat only products that you can pluck, hunt or pick. So basically it's vegetables, meat, fish, spices and nuts.
The benefits of this type of diet is that it's incredibly health, low-carb and high in omega-3 fats (yes FAT IS GOOD!!!) For more information I would suggest Googling it!

As for building muscle; you will be able to combine loosing fat and gaining muscle when you start exercising and doing HIIT however as your body get's used to the exercise this will seize.
There is no real reason for you to start building up muscle if you still have a beer belly to lose. Please get back to me when you feel that you've lost sufficient weight or want to start gaining mass* again.
*By gaining mass I mean both fat and muscle. It is very hard to put one on without the other!

If you have any more questions please let me know.

What order you decide (bulk first or cut first) doesn't matter that much but with that said, I usually actually recommend people focus on bulking first for two reasons

(1) It's easier to bulk than cut so at least that way it gets people into the gym
(2) Once you bulk up some, the losing fat part (the hard part for most people) becomes easier than losing fat when you have less muscle

Of course, I wouldn't suggest this order if someone is morbidly obese or close to it.