What I do is just check out some of the clothes and turn them into work out clothes which works well for me. I personally do not see the need to buy new workout clothes when I can turn a couple of my clothes and save on that money. Well that is just me but I also think in future if it is necessary I might just buy them.
The only piece of clothing that I bought for workout is a sportsbra (Old Navy) and a pair of shorts (Under Armour) I like their quality and the material feels nice on my skin during the summer. Other than that I don't own anything else particular for a workout, like you I just wear my old clothing, like my old T-shirts. I feel a lot more comfortable in them for a workout.