Anything by Adrian Goldsworthy will be good. He's a serious historian and a prolific writer. His books are very good as an introduction to the subject, though if you want to go really deep into the subject you'll need more specialized books.

Some books by Goldsworthy which are interesting:

• The Complete Roman Army (2011)
• Roman Warfare (2007)
• In the Name of Rome: The Men Who Won the Roman Empire (2004)

The focus of each of these books is different but inevitably there will be overlap, so you may not want to read all three of them (on the other hand, you might if you're really interested). Read their descriptions over on your favourite book-selling website to decide which one suits your interests best.

An example of a more specialized book which is still very readable for not-yet-very-experienced historians is this:

• Gregory Daly, Cannae: The Experience of Battle in the Second Punic War (2002)

This book goes into every detail of every aspect of one the most important battles in Roman history, covering the opposing armies and the battle itself. You'll learn an awful lot about the Roman army in this specific time period (216 B.C.), but it won't necessarily apply to later periods.

If you'd like to read a Roman source, try reading

• Vegetius, Epitoma Rei Militares

It's a fourth century book covering how the Roman army works (or should work). It has been translated into English as Vegetius: Epitome of Military Science.

(Edit: spelling, small textual addition)