I have a MacBook Air, 13" model, and I really like the machine! It easily does the things you want, along with many, many other things. My model is a mid 2013 one, and it has a 256 gig SSD inside it. An SSD, in case you don't know, is MUCH, MUCH faster than a standard hard drive.
The Mac Book Air comes basically in 4 'standard" models/configurations:
MacBook Air 11" screen, 128 gig SSD
MacBook Air 11" screen, 256 gig SSD
MacBook Air 13" screen, 128 gig SSD
MacBook Air 13" screen, 256 gig SSD
They are very light, and as I said, very, very functional.
You would need to first decide how big of a screen you want. 11" is too small for me, so that is why I went with a 13" screen.
For the size of the SSD, I got the larger 256 gig drive for the following reasons:
1. I wanted as much free space on the drive as possible. That goes a long way towards minimizing any issues with the machine.
2. I like to watch movies, and TV series (like Breaking Bad, Better Call Saul, The Americans, etc.), and while I have a nice, portable external drive that I take with me (along with my MacBook Air) when we travel, when I need to download something (especially if it is large), I have the extra space on the machine to accommodate such large downloads.
3. There are times where I want to watch a series before I go to sleep, in my bedroom. So, having the series on my Mac makes that a snap.
To give you an idea about prices of the various models, here is a link to Best Buy, that shows various MacBook Air models, in various configurations:
Those prices are not necessarily the cheapest, but it will give you an idea.
I forgot to mention that the 4 "base" models I listed above all come with 4 gig of RAM. For my purposes, that is easily enough, and based on what you said, should be more than enough for your needs.
No matter which Mac laptop your purchase (or, for that matter, any Mac), you will need to perform the following tasks on a "periodic", consistent basis:
1. Do disk cleanup on your own, like deleting stuff you no longer need, moving any stuff you still want to another location, etc.
2. Make backups to an external device. That is so, so critical. There is software to do that, both free (Time Machine, comes with the Mac OS), and paid (SuperDuper! and Carbon Copy Cloner are two of the best).
3. Use disk maintenance/repair software to keep your SSD in tip top shape. Again, there is free (Disk Utility, comes with the Mac OS), and paid (two of the best are TechTool Pro and Disk Warrior). Disk Utility is fine, for most things, but I prefer (and use "religiously") TechTool Pro (I also have Disk Warrior). There is also an excellent freeware product called Onyx that performs some useful, disk cleanup tasks.
Finally, do you use any third party software, like Office 2011 for Mac, VLC media player, etc.? The new machine will come with at least the last version of Yosemite, OS 10.10.5, or a "new" version of El Capitan, OS 10.11.x (the x will either be blank, or a 1, 2, or 3). There is distinct possibility that some third party software you are currently using with OS 10.6.8 will need to be upgraded to work with whatever new OS the machine comes with. If the machine comes with Yosemite, OS 10.10.5, you will have the opportunity to upgrade the OS to El Capitan, through the App Store.