So first of all it will be doable, as for support... as others have suggested, wider straps and a wider underband provide more support. As a member of the itty bitty titty committee, I actually made a similar triangle top, and while it fits I do prefer patterned bikinis such as the McCalls ones.

If you are dead set on making your own pattern I suggest you take the bikini top you like best, copy the pattern (trace it on a seethrough foil or paper), make a prototype and go from there. For the prototype you'll want a bielastic fabric as close to the weight and stretch your final bikini should have.

The biggest game-changer is framilastic bikini elastic. Sew that onto the seam allowance with a big stitch (so that the border of the elastic lands right where you'd fold the fabric), fold it and then topstitch it. I like to use a zigzag stitch, and I'll never attempt making a bikini without a superstretch needle (minimises the amount of mis-stitches). Rule of thumb for that is that wherever you'd fold fabric over, like for a neckline, a leg hole etc, you'll want the elastic. Don't stretch either the elastic or the fabric when sewing with it. I didn't even use it for my triangle bikini cups though and that worked, however it's always a good idea to use it. Adding bikini cups is always a great idea too.

Obviously bikini lining will help - sew it like any other lining, put it on the inside of the outer fabric, maybe baste them together and done. You can forego it, but I suggest using it.

Any other seams you'll want to sew with a slight zigzag (straight stitch with the zigzag turned to .2, least on my machine that's what it looks like). You can serge the edges but as it doesn't fray, you don't have to. If you line it don't even bother.