compact project, powerering and charging

BruceM:
what does LSD stand for??

jremington:
I also have no idea what an "LSD" variant is, but NiCd or NiMh cells will work fine in your project.

Low Self Discharge just like 'MorganS' said, Eneloops for example, Sanyo popularized these in the market but now almost every NiMH manufacturer has their own LSD variants with different names.

BruceM:
I looked up a LiFoPO4. I don’t think that style of battery will work for my project. It looks a little bulky

They are available in a lot of different sizes. 14500 size for example is exactly the same size as a AA battery, 10440 size is exactly same as a AAA battery.