Well, usually the single, non-subjective reason not to use Arch is because the package manager doesn't have package signing, which is kind of a big deal.
If you just want to try it quickly I suggest looking into ArchBang. It's comes with a basic Arch system in a LiveCD environment.
archbang! I've been using openbox on crunchbang (#!) for a bit, its nice too but based off of Debian Stable rather than Arch's rolling release so I don't know how life will be like over where you are.
For one, ArchBang relies on Slim. A project which has some big bugs in it and has been abandoned. Last commit was 2010.07.08. This can cause problems for people. Its still is a problem for some regular arch users.
ArchBang does some strange and wrong things too, like enable all mirrors by default, which I only learned after debugging some pacman problems over irc, where it was spilling over to the next server which was out of sync. idk if thats still the case, but this was only a few months ago.
There are other things too; all small little things that are different and out-of-line with arch upstream that cause problems. So if the dev's want to do things differently than Arch its hard for us to support them. However in practice these are all just corner cases.
ArchBang as a shortcut to a desktop is probably okay if you know what your doing. But it also attracts a lot of less competant users because it seems easier, and this leads to all sorts of problems. They don't know what broke because they don't understand the underlying system. Hiding the system is antithetical to Arch's philosophy so I think its understandable where the frustration comes from when its the Arch community that has to support ArchBang (theres no archbang irc channel anymore, the devs can't staff it, so they wander into #archlinux. We're still mostly helpful).
Why not ArchBang, is similar to Crunchbang but uses Arch Linux as base distribution. Newer package selection though and package management through pacman. Rolling release.
I was going to recommend Arch, since that's what I run on my SL510. If you want something simpler up and running quickly you could always use ArchBang or CrunchBang.
as an Arch user I'm probably biased, but it really isn't anywhere near as much of a timesink as LFS or Gentoo can be. the installer is guided, and the wiki is pretty comprehensive to help you install your basic packages.
if you're just concerned about the initial setup, then check out [this list](https://wiki.archlinux.org/index.php/Arch_Based_Distributions_(Active\)) of Arch-based distros, many of which come with a DE/WM and basic packages already installed.
You could also try Archbang, which is based on Arch Linux. It comes with a preconfigured and I think very nice looking Openbox desktop including Conky and keybindings for most common applications. You won't have apt, but Pacman isn't hard to get used to, plus you get Arch's AUR user repositories, which contain a huge amount of applications and scripts.
Gmail notifications aren't a problem with Conky and as TheVenetianMask already explained, setting up special keys that aren't working out of the box is pretty easy. I'm not familiar with Google Tasks, so I can't comment on this point.
Sorry this comment is not helpful, but I learned Arch with ArchBang! It has a live usb iso with easy installer scripts and once you go through the installation, runs exactly like Arch with lxde and openbox.
E: it took me a few months to acclimate to cli, and once I did, I followed the wiki and installed Arch myself. It was kinda fun and empowering. I feel happier knowing I have nearly direct control over everything in my system.
Search the wiki for details.
Probably the time you have to invest building your system, as a standard install is pretty bare. There may be a bit of a learning curve.
Consider Archbang which is essentially Arch with a bunch of packages preinstalled and configured.
With you on Arch, but jump ahead to the end and just install ArchBang. It's openbox on arch with tint2 as a panel. It's a pretty easy install, decent configuration and puts you hours ahead of a regular Arch install.
Add chromium, LibreOffice and a different panel than Tint2. I use fbpanel because it's easy to configure using a text file, but it's arch, so you can use whatever you like. Install XFCE if you want a more coherent desktop environment. It's quick enough on arch that it will run fine on that machine.
Edit for typo.
Mentioned it elsewhere, but it's worth another comment. Install ArchBang and adjust from there. You get regular arch up and running very quickly. It's lightweight, clean and you can make it whatever you want.
I replace tint2 with fbpanel because it does more and is easily configurable through a text file. However, you can add anything from the arch repositories, so go crazy. You might want to put XFCE on there for a more coherent experience. With arch it's fast enough that it should run fine on that machine.
Others that are little known but mentioned here that deserve a second mention are Salix and AntiX. I'd add Zenwalk, which is very much like Salix. That said, I'd go with ArchBang, because it's based on arch and therefore a rolling release that's easy to keep up to date. Salix and Zenwalk are based on Slackware, so they will be rock-freaking-solid (more solid that arch, in my experience), but kind of a pain to upgrade. AntiX is based on Mepis, and has the best utilities of the lot, but also not as easy to keep current as arch.
It's Arch Linux but pre-configured to use openbox and a similar set of applications as CrunchBang. There's a bit less setup than with straight up Arch and it's minimalist in terms of interface and applications. This doesn't mean that you can't install everything but the kitchen sink if you like. http://archbang.org/
ArchBang would be ok, if the Arch philosophy works for you... it uses about 50MB of RAM at startup, and 'generally works.' I use it on an old laptop, and the only thing I really needed to worry about was downloading the broadcom b43 wireless firmware from the Arch User Repository. http://archbang.org/
ArchBang would be worth trying... http://archbang.org/
I run it on a Celeron M 1500 with 2GB of RAM and a Pentium M 1700 with 2GB of RAM. While I realise I have 2GB of RAM in each laptop, it never uses much of it... the most I've used was about 500MB. At boot it only needs about 50MB of RAM, and it seems to be pretty easy going on memory use.
It is a live disc, so you can try it without modifying anything... and you can load it all into RAM to enjoy some speedy performance ;) The Arch Wiki and Beginner Guide are both so good that the distro can only be considered user-friendly, but you do have to be able to follow simple instructions...