A serger is really nice when you want that clean professional edge to your seams
You could in theory work with only a serger and be perfectly fine.
A problem you might run into though is the fact that it's very compact. Unlike a sewing machine that has that extra 4-6 inches of space between the foot and the body, the serger doesn't have that gap.
So if you were to try and do a straight stitch for an applique you wouldn't be able to use a serger for that.
Or if you were to try to do some type of quilted pattern on fabric for a bag or other item, the lack of gap would prevent you from doing that.
Maybe you just wanna to make a creative texture like this with a contrast thread. (Not my image, found it with google.)
Without a serger you can always use a zigzag stitch to over lock the edge of the fabric and still get a nice seam.
I would personally invest more money in a nice sewing machine with multiple stitches that you can use for all your projects and leave a serger as a later purchase for when you really get into the nitty gritty of presentation.