Inverting, non-inverting, it makes no difference. At the end of the day you just end up with a number.
The simplest circuit for a non-inverting amplifier is:
Your signal comes in to the non-inverting input. Between the output and the inverting input is resistor - R2. The inverting input is connected to ground via resistor R1.
The amplification ratio (gain) is given by 1+(R2/R1), so the output voltage is the input voltage multiplied by that ratio: Vo = Vin*(1+(R2/R1)).
You can use simple high-school maths to rearrange that to get some sensible values for R2 and R1. Here's a clue: pick a common value for one of the resistors and calculate what the other should be - see if you have something close in your box. If not, try another common value. You don't have to get all the way up to 5V - you just want to get it higher than you have at the moment.