Without knowing much about you, it is not possible to say which is the best bang for your buck. Just make sure you check B&H and Amazon pricing, and make sure you compare and understand the features, and the feature differences between the Pentax, Nikon, and Canon models because they vary significantly.
Canon and Nikon have more lenses in their lines, but Pentax makes more than enough lenses to satisfy most amateurs. Most amateurs own 2 or fewer lenses, and many own only the kit lens that came with their camera.
The Nikon 3200 at 24 megapixels has 50% more megapixels than the Pentax, and 33% more than the Canon cameras you might look at, but that's not relevant for most amateurs, and the Nikon's files will require 50% and 33% more storage space.
The Canons you'll be looking at are noisier above about 800 ISO than the Nikon and Pentax DSLRs. If you don't shoot at high ISO, you won't notice this, and you might not notice it at 800 ISO. At 1600 ISO and higher, you will likely notice it.
The Canon sensor has less dynamic range, and will blow out whites and highlights more frequently than the other two brands. If you don't know what to look for, you probably won't notice this either. In practical terms, it means that clouds will often have less detail and specular reflections will be larger and more distracting. Again, if you don't know what to look for, you might not even notice this.
There are also differences in the way the cameras render. I typically prefer the image output of Nikon and Pentax to that of Canon. But you might feel differently. I suggest going over to dpreview.com and looking at their samples. Be careful reading what they say about the cameras, however, because differences between cameras are often exaggerated, and in my opinion, their review summaries and overall ratings are clearly biased toward who is paying them the most ad dollars.
If you want to see what Pentax can do, your best bet is pentaxforums.com. There are lots of images, camera reviews, and lens reviews done by users and by reviewers.
I personally wouldn't go the micro four thirds or smaller route. I frequently shoot in low light, and the smaller sensors in those cameras are significantly noisier at higher ISO and longer exposure. If you shoot snapshots primarily, and don't care as much about image quality (it is the highest priority for me), then the smaller sensor cameras might satisfy you.
A battery, charger, and strap come with the camera. If you have a place to recharge, many people won't need a second battery. But make sure you check how many images you can get from the batteries, because it varies. If you think you'll shoot more than a few hundred images during the day, then you might need a second battery, depending on which camera you buy.
If you're not taking a laptop with you, then you'll need multiple SD cards. I buy only SanDisk Extreme 45MB/s in either 16 or 32 GB sizes. With Pentax, a 16 GB card will hold about 600 RAW images, many more if you shoot jpg only. With Nikon about 400 RAW images, and Canon about 530 RAW images.
Lastly, I disagree with those who say you'll get better images from a compact camera. Pentax, Nikon, and Canon all have idiot proof auto modes that will enable you to get good images, despite your inexperience. Just make sure you read the manual, understand the various modes, and practice, practice, practice before you leave.
