240sxy:
What is a rheostat?
A rheostat is type of a variable resistor. If you are familiar with wall mounted "Dimmer Switches" that control room lighting, those are usually rheostats. Used with an Uno on an analog input pin it could be used to control the rate LEDs flash.
A rotary encoder looks similar to rheostat, but is a digital switch rather than an analog one. Connected to a digital I/O pin could be used to select from a large list of the different patterns you were planning on using.
At this stage in my learning, 500 mA means nothing to me (milliamps I presume?). I'm guessing that this would not be sufficient to run anywhere from 50 to 250 blue LEDs.
Yes on both counts. The symbol for milli-amperes is "mA", and 1 mA = 0.001 A. Also, standard 5 mm LEDs have a current rating of ~20 mA each, and you'll probably want to use brighter and therefore higher current LEDs. Furthermore, you'll need between 100 mA to 150 mA to run the UNO board (this can be reduced some but in your application it won't be necessary). I'll let you do the math on how few LEDs you can power from a 500 mA source.
Additionally, you could choose RGB LEDs instead of blue LEDs. RGB LEDs actually combine three different color LEDs (red, green, and blue) that are blended together to create almost any visible color. These types of LEDs can easily be controlled by Arduinos. However, you might to make your first project more complex than necessary.
From the pictures I've looked at, it appears there are multiple choices for a power source, is this correct? Also, even though I plan on hardwiring the unit, I would like to be able to easily remove it in case I want to reprogram or if I have problems. There is a female port for an outlet adapter which I'd hope would be fairly secure. Would it be possible to buy this adapter and splice it to my 12V car battery? Or just buy the male end and wire it?
As you stated, there are many options. 12VDC is the upper end of the Uno's voltage regulator, so it is possible to power it from a car battery. If you wire directly from the board, you'll want to connect the positive wire to the VIN pin and the negative to one of GND pins. You could also use the barrel jack, there are wires you can buy with the proper plugs on one end and unterminated on the other. Also you could just get a plug for your car outlet, so you don't have to splice into your car's existing wiring.
Do you know of any boards without pre-installed headers? Or any suggestions of a better board for what I plan on doing?
Some distributors sell versions of Arduino boards without headers, but many like the Arduino Pro are not a good choice someone new to microprocessors. So on second thought, a stock Uno is probably the best for you at this time.
Thanks again for your help! As I said, I'm completely ignorant when it comes to anything like this. I plan on using this project as a learning experience which I'll hopefully get something useful out of.
You earlier mentioned your plans to buy an Uno and the "Programming Arduino Getting Started with Sketches" book. That's a good idea, but you might also want to consider the various "Arduino starter" kits available, like those listed below, instead of just an Uno. It will let you experiment with the Uno's capabilities beyond what you'll use in this project.
