You can make almost anything without an overlocker, I make all my activewear, including swimwear, with an overlocker, zig zag and straight stitch.
My techniques aren't just good for items we exercise in, they're just as useful for clothes made from any stretchy fabrics(I mean knited fabrics rather than woven fabrics with Lycra that really need to be treated as if they don't stretch)
Some knitted fabrics stretch hoizontally and other stretch both across and vertically. For activewear you need stretch in both directions as patterns are made with negative ease i.e. smaller than the body they're designed for. Therefore your fabric needs to stetch vertically to allow you to bend over.
My unique Stretch Fabric Ruler is a quick and easy way to find out how much any knit fabric stretches to be sure it's right for your pattern. It's for sale from my shop and makes a great present for sewing buddies.
Read about the techniques I've developed over 40 years of making dance and swimwear as well as how to flatlock with your overlocker from my activewear tutorials page