THIS is what you should use for your diode. 2 dollars more than the LPC-826, but it comes in a COPPER module and it has much better specs. Also, will have slightly lower wavelength (650 vs 660) IIRC which will make for a more visible(slightly) beam.
THIS is the 3 element glass lens for red lasers. You can order it with the diode buy adding one to cart, exiting the new window and then adding the other to the cart. They will both be there.
THIS is the mohgasm JAD kit. For the powers you are at, you do not NEED any upgrades. However you can get them if you see fit. Either get the driver set to 200mA or 378mA. I have mine at 378mA and it has a beautiful beam and just enough burning capabilities that I can make my friends jealous when need be. I would recommend the Black Anodized Heatsink for this build you are doing as it will look very clean, expecially if you get the black focus adapter.
Total Price: 21+9+35 = 65 dollars for the build. Add in CR123 batteries and you are good. Do NOT drive that on one cell as it will be much weaker.
Some advice: I would recommend going with the 378mA current. It is not all that much more than if you went with 200mA, it will give you ~225mW as opposed to ~100mW. Have fun with the build, find ways to make it your own. At the end of the day do whatever you want to with your build. The above are just suggestions based on what I find I enjoy, your mileage may vary.
But I can guarantee that DTR's low divergence diode I linked will be a much cleaner dot and better beam than the LPC. The LPC has little wings through the dot, the DTR Diode does not.
Hope that helps,
Isaac