Check the LED UCL DIY As far as I know, there's no good way to retrofit LEDs into your halogen pucks. The DIY should answer everything else.

The main choices are between low voltage and direct wire lighting. The diy Ucl thread on this forum and the follow on thread have more details

I don't know how the IKEA LED strips compare with the non-IKEA ones but I wasn't drawn to them, and I'm pretty pro-IKEA and value driven (as opposed to low-cost driven, that is, I love lower cost but only if it's a good value). I suspect they are just LED tape strips, and I had decided I wanted bars and not tape. As for installing lights inside a piece of furniture, have you considered the stick-on lights that you can put anywhere and that are either battery-operated (so you can swap out batteries when the lights dim) or LED? They are usually sold in 3-packs at Bed Bath, Home Depot etc. and are not expensive, we put them inside our last kitchen's dark cabinets and they really kept us sane when looking in the back (and in our new kitchen we only did drawers and pull-out cabinets on the deeper bottoms, and regular cabinets up top, so we don't have that issue anymore). Follow up - I wavered between Environmental Lights and Juno, both with a dimmer, and ended up having the Juno's installed and decided I hated them, but couldn't afford to uninstall them and install the Environmental Lights, so returned the Environmental Lights and lost a restocking fee and shipping but was impressed with Environmental Lights overall and how they were helpful and customer service oriented and would seriously consider buying from them in the future - but I can't speak to how the lights would have looked or worked. As for the Juno's, I now fairly well love them, they are fully dimmable piece by piece and turn off piece by piece so the look is customizable from hour to hour, and when all 3 fixtures are turned on at the wall switch and fully "on" the light is brilliant and dramatic. So I'm fairly happy with them but not thrilled with Juno overall - the Home Depot dimmer-dial model I bought has NO diffuser which really hurts the eyes when used with a shiny quartz countertop (I used the Environmental Lights diffusers out of frustration), and Juno's customer service people had no fixes and no suggestions for this problem, and basically wash their hands of these models since they are the "Home Depot brand". Plus Environmental Lights responds to emails on weekends and Juno has no customer service outside of business hours. Overall while I like the Juno lights fine, I prefer Environmental Lights as a company.

What is being referred to as "Xenon" here is really incandescent bulbs. Smaller incandescent bulbs (like the type found in old-style flashlights for example) have a much lower color temperature, and as a consequence the light typically feels very orange-colored and dull. Bulb designs filled with Xenon gas help compensate for this, to some extent. I can get much more into the technical details if you want, but that is the basics of it. In general though, Xenon will still give off a lower color temperature than halogen, so if you really want a brighter whiter color of light, Xenon is probably not the best option. LED is probably the best option for undercabinet lighting, but can oftentimes be overly pricey. If color rendering is an important consideration, you might want to look into high CRI LED lighting, because under regular LED lighting colors can appear just a little grey-washed or yellowish. This is likely to be even more pricey though. Incandescent bulbs (which includes Xenon and halogen) are just not particularly well suited to undercabinet strip lighting. For one thing, when there are multiple bulbs each with a lower wattage, the color of light is confined to the very warm white color territory. Then there are always bulbs burning out that need to be replaced. There are many different options, and they all carry their own subtle advantages and trade-offs. All undercabinet lighting is kind of overpriced, in my opinion, so unless you are really looking to create a dream kitchen, you might want to consider going without it.