Several things are quite clear with your photograph and consideration of options.
1. You are correct that you would be best with just an augmentation as long as you realize what a breast augmentation with implants will do. It will fill out your breasts and increase their size by a cup size (the minimal). It will give the appearance of a lift because of the filling out but will not actually lift them. It will make your areolas look smaller in proportion to a larger breast but will not actually change it. It can be done with as small a scar as 2 cm in the crease below the breast. But it will not bring your breasts closer together, correct the asymmetry, or change the position of the breast on the chest wall. If an implant is going to fit and look natural it has to fit and act like a pillow behind your breast.
2. Augmentation and lifts are two different procedures that do two different things and tend to work against each other which adds to the complexity, unpredictability of the result, and increases the chances of problems and revisional surgery. Your breasts are not low enough (ptotic) to benefit from a lift at this time. That could change but an augmentation now is simpler and will solve more of the issues you're concerned with. Aside from possibly scaling down the size of areola, a lift, regardless of the type, will result in a scar around the areola and will accomplish little else.
3. So-called Crescent Lifts do not work and have been abandoned by experienced breast surgeons. The nipple/areola cannot be truly or reliably moved without a full release of the nipple/areola and the breast from the overlying skin and reposition it. Even a circumareolar (periarolar, Benelli) lift will not accomplish what you would like to have in terms of nipple/areola position and no lift procedure (or implant procedure) will tighten anything. Tightness created by surgery is an illusion.
So a lift is not required and I would not recommend it at this time although it might be helpful in the future. An augmentation, probably using lowest profile silicone gel implants because of the lack of tissue coverage and lateral breast placement, would give you the most improvement for the least surgery and scars. Be sure the surgeon matches the width of the implant to the width of your breast.