It will be difficult to make a full penetration weld on that material with that machine. However you can make a satisfactory partial penetration weld with 0.030" and C25. There's little advantage to change to 0.035". You won't notice a difference between ER70S-3 and ER70S-6.
Burn-back (to the tip) is caused by wire melting faster than wire feeding. So you have 2 options: #1 - Decrease voltage (wire melting) #2 - increase speed (wire feeding). I favor turning settings up, it seems more forgiving. I have found these size machines run well at the mid setting point. (4 on a 1-10 scale)
Start with a new contact tip. Don't file or grind the old one. The frustration is not worth saving $0.75. Make sure the tip is 0.030". Make sure the drive rolls are 0.030". Make sure the drive rolls are tight enough to grip the wire. I never use those 1lb rolls. The wire has too much helix & cast (bend). I'd use the largest size roll that will fit. Make sure the torch has relatively straight path. Don't stand on the torch. (More common than you'd think)
Then it's all up to you finding the proper CWT (contact tip to workpiece distance). About 3/8-1/2 inch is a good start.