When you don't have a very powerful machine it's important to make sure that you realize the limitations. I run both a new MacBook Pro R that is as loaded as you can build one and a 2011 Mac Mini with 16GB of ram. For a lot of my tutorial work I use CC2015 and the Mac Mini because it's plugged into a 1080 X 1920 monitor and it's easier for me to make the screen recordings and I want to make sure that most folks can follow along on a pretty basic machine. The Mac Mini works just fine and is completely within my expectations for a machine with so little power because I've set it up to use everything it's got in the most efficient way I can. You want to check to make sure that you are not starving the OS and other apps and that you are using the right number of CPU's with your memory setup, and you have to adjust your workflow so that you do most of your motion previews at half resolution or less. Do that by setting up the comp panel resolution to Auto and keeping the Zoom factor at 50% or less for checking motion. Trying to run a 4K project on the Mac Mini or your older machine at anything more than a zoom factor of 25% and 1/4 resolution (auto) would not be a very efficient way to work, but then again, when you're working in AE you should not yet expect to run all of your previews and animation tests at full resolution. I've never done that. You just have to learn how to work efficiently with the hardware you've got.
For years my standard workflow kind of follows a traditional cell animators workflow. Pencil test, then ink and color and then photograph the cells. My pencil test is to check animation and timing and it is always done with no effects and low resolution. When the timing is right I start adding effects and, just as a cell animator would do, check the most important frames by closely looking at things at 100%. I don't run previews at 100%, I just check the important parts of the animation. Lastly I render and then check my final output.
One more thing, I seldom make much more than a single shot in an AE comp. Occasionally I will put together a short sequence, but most of my AE comps are under 10 seconds. I finished one tonight that was only 75 frames. Almost all have handles (extra frames) and I do the editing in Premiere Pro. It's a much more efficient way to work. I see folks all the time that are trying to do five or ten minute movies in AE. IMHO that's no way to try and make a movie and it's no way to make a living. Maybe AE will get fast enough one day so you can efficiently put together longer sequences but in most cases, unless you are a magic editor and nearly perfect story teller, you'll be better off doing your editing in a NLE where you can easily make changes and come up with different versions of your story.
Here's the setup for the Mac Mini and CC 2015 and 2014;
2014 when MP is turned on (usually it's turned off):
You should check out this link: Optimizing After Effects Performance - Adobe Support
I guess the long and short of this post is that you can successfully and profitably run AE on a machine that meets the minimum system requirements if you adjust your workflow to match the machines capabilities. The decision to invest in such a machine is going to have to be yours. The better you are at business decisions the better your decision will be.
My DI just finished rendering so back to work. I've got 6 more comps to complete before I catch some sleep.
There are some issues with running AE on Macs - some especially with the latest version of AE and some especially with the latest Mac OS. (There's been some pretty buggy stuff lately from places that usually aren't so bad...) Adobe is putting out an update at the end of this month that they say fixes a LOT of bugs, so it may perform better after that update.
In the meantime, you could try running CC 2014 or CC on that system to test it out. And don't update to a different version of the OS. If it's running Mavericks, stay with that for the moment.