For AAA size, the Thrunite Ti HI is on clearance under $20. It has a cool white XP-L HI, titanium body, and the modes of a Ti3. The Astrolux A01/BLF A01 is an inexpensive high CRI option.
For AA it is hard to beat the Zebralight SC5W. Neutral white, high customization that includes multiple sublumen modes, solid build quality, fantastic efficiency and lumen output all come together to make an excellent EDC.
The L3 Illuminations L10/L11C are basic but effective and affordable high CRI options in this format.
CR123A I'm not as familiar with but I have and enjoy my Olight S1. The Eagletac D25C is another good option.
Hope that helps!