The snowball / avalanche methods for paying down loans is pretty good. Plenty of calculators /spreadsheets online if you Google them. TLDR: pay down the highest interest one first, then put that loan's payment as an extra payment to the second highest loan, etc etc. By the end you're putting the whole 3k into the last loan each month. If you really want to go savings-heavy, keep that loan payment going as a straight-into-savings path and keep living like you were.

Whether or not you put a lump-sum payment at the beginning or not is up to you, but definitely save the 3-6mo worth of expenses and make it a habit to rarely-if-ever touch that.