Hand Sewing or Machine Sewing–What to learn first
With newer sewing machines it is possible to make a garment completely by machine. Machine blind stitches make great hems. Some clothes, such as casual pants look good with a straight stitch hem. You can even sew buttons on with a special sewing machine attachment and many newer models feature these. If you are new to sewing you may be tempted to never try hand sewing, but I feel this is a mistake.
Hand sewing takes time to learn, but it is worth the effort. Many fine garments need that extra touch of hand stitching. Facings may need to be slipstitched in place. A delicate fabric in a fine bridal garment is best be hemmed by hand. Tailored suit skirts and pants are also often best hemmed by hand and if you get into actual tailoring, you will want to learn some hand tailoring techniques. Drapery and upholstery projects may also require hand work.
Ideally, I think you should learn hand sewing techniques at the same time that you begin sewing on the machine. Imagine how proud you will be to display your first project, complete with fine work you have did by hand. To avoid frustration and wasted fabric, I recommend practicing such techniques and blindstitching and slipstitching on scrap fabric, before attempting it on your project.