What is the best way to find the resistances values quickly?
You won't get 300 / 200  / 400 ohms simply by two resistances. Commercially 1k and 100k are available.  But 200k, 300k those are not available. You need to make some series or parallel combination.    

So, the best way is to use either 100 / 1k / 10k / 100k /1M to make any circuit. If you need 100x gain.  Use Rf = 100k, Ri = 1k.   

For 300x,  Rf = 100+100+100. Ri = 1k.   

For 400x, Rf = ( 100 + 100).  Ri = 1k || 1k.  

If you want, you may use programmable resistance IC.