I just published a new project, how you can easily build a nice table light from a cheap candle holder you get in any IKEA shop. The project is using a NeoPixel ring and a Adafruit Trinket as microcontroller.
The microcontroller is very limited, but you will find ready made software which will get most out of this small chip. The lamp comes with 50 different colour modes. There are of course a number of static colours, but also animated rotating patterns. Also there are a few fire like random flickering modes. But of course you can reprogram everything easily to add more of the effects you like.
This time the components are relatively cheap. If you have some spare parts left, the total cost for a whole lamp should be less than $40.