For a Linux laptop, your laptop isn't great, but it isn't terrible either and should be more than capable of running any distro you want just fine. Lubuntu and such are actually geared towards even older, slower hardware than you have.
Mint and Lubuntu both have a more familiar interface, which is good, however, Lubuntu lacks some of the more modern graphics acceleration that your APU can take advantage of so in terms of speed and battery life I wouldn't be surprised if they run neck and neck. If you like Lubuntu, you may also want to try Peppermint, it's like a tweaked Lubuntu. If you use Cinnamon, disable the animations, it will help speed it up a bit. Regarding Deepin, it looks really cool and has some neat features, I like the sidebar, but I found it not nearly as polished as other desktops in many areas, the same applies to Elementary but it's another you may want to try in a quest for something new. While most distros use an older style taskbar with large tabs, many have an alternate version with grouped icons like Windows uses and there is also Mac style docks you can use on any distro. Your choices are actually huge.
My advice, try a bunch but stick to the Ubuntu family and kin such as Lubuntu, Peppermint, and Mint. Support is better, not just in terms of help, but in app support as well. You may want to install Virtualbox to make this easier and faster. You can install a bunch and flip back and forth without constantly re-installing. When I got serious about switching one thing I did that helped was to install the ones I liked in Virtualbox, and then install all of my programs and kept notes. This way I could see which ones had problems and could be corrected and which were show stoppers, it also meant that I knew exactly how to do get everything set up when I did my final install, in fact I was quite comfortable by then.
Here is a list of Ubuntu based distros:
http://distrowatch.com/search.php?ostype=All&category=All&origin=All&basedon=Ubuntu¬basedon=None&desktop=All&architecture=All&package=All&rolling=All&isosize=All&netinstall=All&status=ActiveI would also recommend downloading something like Macreum Reflect, Active Disk Image, Acronis, etc.. and imaging your current drive, just in case you want to sell it, or return to Windows for some reason.
By the way, you can expect to lose 30-40% battery life unless you do some tweaking.
If you want, I can send you my step by step notes on dealing with this, takes about 10 minutes but gets back most of what you lost. I may polish it and post it anyway for those interested.
