Hail Caesar is primarily designed for club or team games with two or more players a side and an umpire. The umpire would generally arrange the game, determine the sides, scenario, victory conditions and so on. The scenario battle reports in the book demonstrate how this is done. Those are the sort of games we tend to play here amongst our friends.
We occasionally play one on one - or without the benefit of an umpire - in which case we would just select forces of roughly equal size and more often than not we would play a simple encounter battle with opposing armies lined up on opposite sides of a table.
To help players get an idea of the the sort of stats we'd use and the values of opposing troops I have written a set of army lists - the first part of which is available on pre-order (I'm attending to the editorial corrections at the moment in fact). This covers 'biblical' and 'classical' armies up to about 250AD - 63 armies in total - and the second book will cover 250 AD - to about 1200 AD. It includes points values for those who want to make use of them - and explains how to calculate them should people want to adjust details more to their liking. This enables you to select forces in the same fashion as most other ancient wargames if that suits you best.
You asked a similar question on the Black Powder Discussion section as well. The answer I gave you there pretty much stands here too. All the same resources for scenarios and I even referred to Hail Caesar in that post too.