Which ten commandments do you follow?

Because the Ten Commandments were given to Jews, to be followed by Jews.

They were given to the Jews. They are reasonable guidelines for any and all.

But they still do not conflict with the 1st Amendment since it is simply a proscription on Congress.

Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.

I don't understand how you don't see the contradiction inherent in the statements "nobody can worship anybody but me" and "people must be able to worship whoever they please."

The Ten Commandments were given to the Jews. They are good guidelines for anyone

Of the two different sets of commandments in the bible which one is that which must not be broken and which one do believers in the inerrancy of the bible follow?

Thou shalt have no other gods before me.
Exd 20:4 Thou shalt not make unto thee any graven image, or any likeness [of any thing] that [is] in heaven above, or that [is] in the earth beneath, or that [is] in the water under the earth:Exd 20:5 Thou shalt not bow down thyself to them, nor serve them: for I the LORD thy God [am] a jealous God, visiting the iniquity of the fathers upon the children unto the third and fourth [generation] of them that hate me;Exd 20:6 And shewing mercy unto thousands of them that love me, and keep my commandments.Exd 20:7 Thou shalt not take the name of the LORD thy God in vain; for the LORD will not hold him guiltless that taketh his name in vain.Exd 20:8 Remember the sabbath day, to keep it holy.Exd 20:9 Six days shalt thou labour, and do all thy work:Exd 20:10 But the seventh day [is] the sabbath of the LORD thy God: [in it] thou shalt not do any work, thou, nor thy son, nor thy daughter, thy manservant, nor thy maidservant, nor thy cattle, nor thy stranger that [is] within thy gates:Exd 20:11 For [in] six days the LORD made heaven and earth, the sea, and all that in them [is], and rested the seventh day: wherefore the LORD blessed the sabbath day, and hallowed it.Exd 20:12 Honour thy father and thy mother: that thy days may be long upon the land which the LORD thy God giveth thee.Exd 20:13 Thou shalt not kill.Exd 20:14 Thou shalt not commit adultery.Exd 20:15 Thou shalt not steal.Exd 20:16 Thou shalt not bear false witness against thy neighbour.Exd 20:17 Thou shalt not covet thy neighbour's house, thou shalt not covet thy neighbour's wife, nor his manservant, nor his maidservant, nor his ox, nor his ass, nor any thing that [is] thy neighbour's.

For thou shalt worship no other god: for the LORD, whose name [is] Jealous, [is] a jealous God:
Exd 34:15 Lest thou make a covenant with the inhabitants of the land, and they go a whoring after their gods, and do sacrifice unto their gods, and [one] call thee, and thou eat of his sacrifice;Exd 34:16 And thou take of their daughters unto thy sons, and their daughters go a whoring after their gods, and make thy sons go a whoring after their gods.Exd 34:17 Thou shalt make thee no molten gods.Exd 34:18 The feast of unleavened bread shalt thou keep. Seven days thou shalt eat unleavened bread, as I commanded thee, in the time of the month Abib: for in the month Abib thou camest out from Egypt.Exd 34:19 All that openeth the matrix [is] mine; and every firstling among thy cattle, [whether] ox or sheep, [that is male].Exd 34:20 But the firstling of an ass thou shalt redeem with a lamb: and if thou redeem [him] not, then shalt thou break his neck. All the firstborn of thy sons thou shalt redeem. And none shall appear before me empty.Exd 34:21 Six days thou shalt work, but on the seventh day thou shalt rest: in earing time and in harvest thou shalt rest.Exd 34:22 And thou shalt observe the feast of weeks, of the firstfruits of wheat harvest, and the feast of ingathering at the year's end.Exd 34:23 Thrice in the year shall all your men children appear before the Lord GOD, the God of Israel.Exd 34:24 For I will cast out the nations before thee, and enlarge thy borders: neither shall any man desire thy land, when thou shalt go up to appear before the LORD thy God thrice in the year.Exd 34:25 Thou shalt not offer the blood of my sacrifice with leaven; neither shall the sacrifice of the feast of the passover be left unto the morning.Exd 34:26 The first of the firstfruits of thy land thou shalt bring unto the house of the LORD thy God. Thou shalt not seethe a kid in his mother's milk.

Exd 20:13 Thou shalt not kill.Exd 20:14 Thou shalt not commit adultery.Exd 20:15 Thou shalt not steal.Exd 20:16 Thou shalt not bear false witness against thy neighbour.

I still don't see a conflict here, unless your trying to create one.

Of course, there are stipulations for not following God's Commandments

In this case, unlike so many other such passages, these are not mutually exclusive. The ones in Exodus 34 and Deuteronomy do not conflict in major ways with those in Exodus 20, they expand, cover different areas, but don't contain the direct conflicts seen in the flood tales or creation tales

Exd 34:1 And the LORD said unto Moses, Hew thee two tables of stone like unto the first: and I will write upon [these] tables the words that were in the first tables, which thou brakest.

I would say this makes for a huge conflict.The "words that were in the first tables" means ,to me, that the duplicate should be a faithful copy of the first.

If an oral history was being recorded to combine various cultures together then let us ask this question.

Which cultures are represented by the two different commandment sets and why are they said to be the same {EXD 34:1} by the god that supposedly unites them?

You say the commandments were written for the Jewish people yet they are told two different sets of commandments.No wonder they are a rebellious lot.