Sigelopisan, are you sure you're Type 2? You're describing a very common pattern for LADA/Type 1's. I was misdiagnosed as Type 2 and did fine on oral meds for 15 months when my blood sugars started going through the roof. Can you get antibody testing and c-peptide? Your doctor is wrong, insulin is the best treatments if oral meds don't work, and if you are in fact, Type 1 that is exactly what you need.
Some people start on either long acting or fast acting, but in time you will need both. Which you start depends on where your problem times are. If your fasting and between meals are ok and you go high after meals than you need bolus (fast acting). If the reverse, then you need basal (long acting). If your numbers are high at all different times you need both.
Calculating insulin dose by weight is not very precise. Starting with "5 units" and climbing isn't good either. Yes, for basal that would make sense (start with 5 and go from there). For bolus you need to figure your I:C ratio so you can dose according to what you are eating. I know I'm throwing a lot of unfamiliar terms at you. I strongly suggest you get the book Using Insulin by John Walsh.