It depends on what the intended use of your computer is.
For example, if you want to have the absolute lowest power consumption, you could get the Pentium M Dothan with a 400MHz FSB. If you want more performance but still low power you could get a Dothan with a 533MHz FSB. In general, Pentium Ms are great for small form factor PCs, and especially media centre ones for the living room. Pentium Ms are becoming more popular in the desktop market thanks to AOpen who have been building motherboards for them. As such these notebook chips are easier to use on the desktop. o1die describes the lengths you need to go to to get an AMD Turion onto desktop such as special heatsinks. AOpen generally include heatsinks with their Pentium M motherboards. The Dothan, especially the higher models offer good performance in most applications and games, but are weak on media encoding.
If you want to save money, you can follow Crashman's advice and get a lower end AMD64. They are definitely cheaper, and can offer better performance depending on the model your comparing to. While they generally only use a little bit more power when idle, their power consumption at full load is more than double. To avoid being yelled at by AMD supporters, I'll reiterate you can get a lot more performance for the same price by going with an AMD64 instead of a Dothan. It depends on how badly you need to keep power consumption down.
If you are concerned about power you should also carefully pick your components. High end graphics cards can quickly use so much power that your choice of processor is irrelevent. Something like the nVidia 6600 offers great performance while having low power compsumption.
Power comsumption can also affect your motherboard choices. For instance, since the Pentium M is a mobile processor, AOpen offers mobile motherboards to go with them. These motherboards offer lower power consumption compared to their desktop counterparts. The 915GM (M for mobile) also offers integrated graphics. If you aren't planning to play many games this could be a great option since the graphics barely increase power usage. Of course, going with mobile products like the 915GM and the Pentium M increases cost.
These two articles offer some power comparisons:
http://www.tomshardware.com/howto/20050621/37watt-pc-16.html
http://www.xbitlabs.com/articles/cpu/display/pentiumm-780_9.html
A good spread of performance comparisons is here:
http://www.anandtech.com/cpuchipsets/showdoc.aspx?i=2382&p=10