The priest may proclaim all the scripture readings, but it is preferable that you ask friends or relatives to read the Old Testament, New Testament and Petitions (or Prayers of the Faithful), provided you can be assured they will do well.
The priest (or deacon) alone is to proclaim the Gospel.
Readers do not have to be of the Catholic faith though they are to be a church-going Christian who regularly hears the Word of God. Suggested Scripture readings may be found on this website under "Readings & Petitions." You are to select one reading from each section; Old Testament Reading, New Testament Reading, Gospel Reading and Petitions (or Prayers of the Faithful).