Your terminology is mainly correct.
Typically, a GATT database has the services 0x1800 (Generic Access) and 0x1801 (Generic Attribute) at least. The Generic Access service contains two mandatory characteristics: Device Name and Appearance. The Generic Attribute service should be empty.
Therefore, the minimal GATT database looks like this:
Handle Description
0000 Service: Generic Access (1800)
0001 Characteristic: Device Name (2A00, readable)
0002 Characteristic Value (string)
0003 Characteristic: Appearance (2A01, readable)
0004 Characteristic Value (16bit enum)
0005 Service: Generic Attribute (1801)
After these two services, you can add your own services. In your case, you don't seem to target a well-known service, so you'll create an own one.
First, create a 128-bit UUID, for example using the uuidgen tool on your Mac's command line
$ uuidgen
DCDF2725-56C8-4235-A4BC-F7951D5C3762
This will be your service UUID
0006 Service: Custom defined Service (DCDF2725-56C8-4235-A4BC-F7951D5C3762)
Then, you mentioned that you want several writeable characteristics. So, let's create another UUID for that one.
$ uuidgen
4C06C6F4-C90D-4C58-8E31-20C8C74FF832
And add a characteristic to the service
0007 Characteristic: Custom Characteristic (4C06C...FF832, writeable)
0008 Characteristic Value (hex, 20 bytes)
Your characteristic value shouldn't exceed 20 bytes, and you should select "Write Request" to ensure that acknowledgments of writes are sent to the central. If you choose "Write Command", writes may be discarded by either your phone's stack or the peripheral.
After you have defined this characteristic, you are ready to start coding.
I don't know the BeagleBoard SDK, but typically, you start by initializing the GATT library and additional modules (for example, to support writes, you have to initialize a second part of the library).
After this initialization, you register your GATT database. If you don't have a nice tool for generating the binary data, you may have to write them yourselves. That's explained in the Bluetooth Core Spec V4.0. Let's hope you can find an API that does the transformation for you :-)
When the registration is successful, you'll have to set the advertising parameters and can start advertising (consult your SDK's documentation and samples for this, again).
What happens now, is that at some time, you will get a callback that a connection has been established, and later, you'll get an attribute request for a given handle. Then, you just have to process the request by looking at the handle, the supplied value and the type of the operation (read / write). Don't forget to always return a success value or an error code in response to the request, as otherwise, you'll lock up the Bluetooth communications.
Normally, those Bluetooth chips always work with asynchronous operations. You'll send a request, and then have to wait until the request is completed before sending the next one. Remember that when programming, it saves you time :-).
If you want to try on Android first because it's more familiar for you, you can try the Galaxy S 4 with Android 4.2. It also has an LE peripheral mode - I haven't tested its reliability, though. The most reliable smartphone stack at the moment to act as LE peripheral is currently in iOS 7 - so it may be worth picking up an iPod touch if it's affordable to play around with it.
