Our Gemara on Amud Beis discusses the situation of a Red Heifer; if he found another animal choicer than it, there is a mitzvah to redeem the first one and purchase the choicer one with the money.

From this Gemara we see a principle that one should always look for the choicest animals for a sacrifice, and when possible even upgrade after the fact. 

Yet this contradicts another teaching from Shavuous (15a) regarding Nechamia’s choice of animal for sacrifices:

The verse (Nehemiah 12:31) states: “And I placed two large thanks-offerings, and we went in procession to the right upon the wall.”

The Gemara questions rhetorically, in what manner were these sacrifices “large”?

“If we say that he took animals from among the largest and the finest quality of their species, Is the size of the offering of any importance before Heaven? …one who brings a substantial sacrifice and one who brings a modest sacrifice have equal merit, and both offerings are accepted as having a pleasing aroma, provided that one directs his heart to his Father in Heaven.”

From this Gemara we see a different principle of modesty and reservation in offerings and worship.

Tosafos there answers the contradiction with a distinction between the action and the subsequent attitude. Yes, it is appropriate to choose the highest quality for worship, however to brag about it is a problem, therefore the Gemara rejects the possibility that this was the largeness that Nechemia was referring to.

This is an important challenge in religious practice. Anyone who takes an endeavor seriously also feels proud, and in a way, ought to. Yet pride is dangerous - especially in spiritual matters because it aggrandizes and emphasizes a sense of entitlement which propels a person away from God. The more a person is stuck in ego and other self concerns the more he is blocked from perceiving and benefiting from God’s subtle emanations. The physical occludes the spiritual in the same manner that white noise drowns out sound. It is not an accident that Moshe, the greatest prophet who saw the most of God that a man could see (Bamidbar 12:8), was also the “most humble of all men (ibid 12:3). His great humility allowed him to disconnect from his self enough to perceive God.