The arduino doesn't cost much, for about $15-$20 it should be possible to buy one.
For the finished project itself you may not need everything on the Arduinos PCB though.
For $3-4 one can buy a smaller micro controller powerful enough for your project, You also would need to create your own board which perhaps could be done for about $3-4 as well.
Problem with this solution is that you probably need to search/read/understand loads and loads of info to get your first program burnt on chip. With a standard board being just a few bucks more expensive it may not be worth the trouble, certainly for a first project. A ready built board with standard controller is much more forgiving, it's a matter of connecting it to the PC, writing your sketch, choosing the right board in the IDE and uploading your program.
Getting suggestions to program the board...
Problem with a lot of projects is that they each got their individual requirements/ specific components and way of programming. A lot of what you want to do you'll have to find out by yourself.
Personally I would... start with the Arduino tutorial ( http://arduino.cc/en/Tutorial/HomePage) to get a little acquainted with the board and the way of programming.
It won't immediately help you with your project, but it will tell you most basic parts even if you don't follow every part of the tutorial.
Next I'd find out how... to work with each individual part of your project. Connect an LDR to the arduino and write a program to just display the level of light on the LDR to your computer screen. You could try to write a routine after that that displays something like "I haven't received any gifts recently", "I just received a gift, but there's still room for more" and... one that says "I'm probably full" if the beam's interrupted for more as 10-15 seconds.
Checking SteveUKs suggestion to see what effect ambient light levels have could be done here as well.
If the side opposite to the LDR reflects too much light, painting it black may be needed.
After that I'd start checking how.... to connect the Xbee if you choose to and how to communicate with it. It basically uses a serial port and you'll need to configure two of 'm to work with each other using AT-commands. Personally I haven't used one yet, I'd collect every datasheet I could find on it and google "xbee arduino" a lot.
Once you get communication working, you could start merging the LDR- and xbee- program.
Quite a lot of info can be found on the playground Arduino Playground - HomePage, but it can sometimes indeed be hard to find exactly the info you need.
The "World Famous Index of Arduino & Freeduino Knowledge" http://www.freeduino.org/ may give you a lot of info as well.
Personally I often just start googling, quite a lot of people use Arduino for a lot of projects and even googling "Arduino fridge" for example gives a load of results. Quite a lot of info can be found on the Arduinosite, but If you don't know how to connect an LDR or can't find it here, just google "arduino LDR Schematic". You may end up on a page of someone using LDRs for a photography-project or a light-seeking robot, but that doesn't matter much. If the page has some arduino code as well, you could
delete the robot/photography part and adapt it to your purposes.
One thing I wouldn't do is start buying expensive stuff.
I'd probably would buy the arduino since you'll need one, but... I'd check most requirements before starting to build the project. For example, what is the distance of the bin to the electronic part receiving messages ? If it's less as 300 ft xbee probably will be able to handle it. If it's not you might... buy two expensive modules which aren't capable of performing the task you have in mind for 'm.
How... would you like to warn the people who have to empty the bin ? If they would need to receive an Email while being miles away you probably need to include an ethernet solution, but if they only need to see a light telling it's full or not you may not even need an Xbee, it may be possible to adapt a cheap transmitter/receiver circuit to open garage doors or... as I suggested as a joke just sound a small siren without any other wireless stuff.