If you -really- want cheap and small, get a 10-pack of "fauxtons" from DX for $4.50 or so. They lose brightness fairly rapidly (coin cell batteries) but put out a still-usable amount of light for quite a long time. At 45 cents each you can stick them everywhere, give them to your friends, etc.
E01 is basically similar (5mm led) but runs on an AAA and is more durable. It will run for about 8 hours on a cheap alkaline AAA without dimming, and is bright enough for most short-range (e.g. indoor) uses. It's not a searchlight.
ITP is conceptually different, a LOT brighter and with a cleaner beam, but more power-hungry and demanding towards batteries. You can use an alkaline in it but it will dim rapidly. You can use an L92 lithium AAA for good performance (yet still comparatively short runtime compared with the E01), but those are pretty expensive and wasteful if you use a lot of them. So you really want to run it on rechargeables, which means you need a charging system and a certain kind of personal involvement with the light in order to keep feeding it. That in turn will affect your thoughts and dreams so you will keep buying more and more lights, posting photographs of them, building your own, etc. A person who does stuff like that is called a "flashaholic" (we hang out mostly on this forum) and if you want to become one of us or are one already, then that's great. But it's not clear what your goal is.