The problem with this question format is the majority of the best and cheapest CD printers are now out of production. :sad:
If you live outside of the USA chances are good you can buy a Canon ip4600 for $100 USD or less, and this is their only current inexpensive CD printing model. But in the USA Epson licensing prevents Canon from adding that feature, and so far there is no firmware mod that can fix this. If you can find old stock of ip4500s or MX-850s, they CAN be modded.
In the USA the Epson 1400 printer and Artisan 700/800 MFCs are the only widely available CD printing models. There may be some factory refubished R280 printers and the (IIRC) 595 MFCs still available.
HP makes a few CD print capable units but these should be avoided due to many reports of poor printing results.
To answer your original question:
IMHO, the BEST and CHEAPEST CD printer is a tie between the Epson R220 and the Canon iP4500 (with the UK CD tray mod performed).
Got the R220 on closeout at Wal-Mart 3 years ago for $50 and a set of refillable carts with enough bulk ink for 12 refills for about the same.
Got the Canon iP4500 for $79.99 delivered and a UK CD tray for $22 on Ebay. Won't use until the Epson wears out but there is plenty of good bulk ink available at low prices to match the R220's thriftiness.
But... these models are no longer manufactured. The iP4500 can still be found new on Ebay but for quite a huge markup. The R220 and similar era Epsons will only be found used or as non-factory refurbished.