I'll preface this by saying that firearms are not my specialty, so if anyone with a better handle on the subject wants to chime in, feel free to!

Essentially, the army kept using the New Land Service pattern musket, virtually unmodified since the Napoleonic period, until 1839. In that year, the weapons were converted to Percussion cap firing types. In 1842, a new pattern Percussion musket was introduced, in its length, weight, and calibre of bullet fired exactly similar to the flintlock conversions of '39. The muskets were never issued all at once, and many troops continued to use the old flintlocks well into the 1840's.

The rifles, meanwhile, continued to use the Baker rifle. Improvements to the priming pan, lock, hammer, and bayonet were introduced in the 1820's. In 1837, the Corps adopted the cumbersome Brunswick rifle, which fired with a percussion cap mechanism.

In 1851, the whole of the infantry adopted the Minie Rifle. This was the weapon carried initially into the Crimea. It is notable both for being the first rifle issued universally to the infantry, but also for the conical shape of the bullet fired. The Minie rifle was destined for a short life: in 1853 it was superseded by the muzzle loading Enfield Rifle.

As implied by the preceding sentence, all these weapons were muzzle loaders. It was only until 1866, that the infantry received a breech loading rifle in the form of a conversion of the 1853 Rifle with the addition of the Snider patent breech.