A shirt dress is really a shirt that's decided to stop being sensible and go all the way down past the knee, which means it does the job of a shirt and a dress at once: buttons you can adjust depending on the weather or your mood, a collar that makes anything look a bit more put together, and enough length that you're not thinking about it all day. It's the dress you reach for when you want to look like you've made an effort without actually doing anything complicated.
If you haven't got one yet, start with something in a cotton or a cotton blend that has a bit of structure to it, not so stiff it stands away from you, but enough that it doesn't cling or crease into a crumpled mess by lunchtime. A midi length is the easiest to live with, long enough to wear with bare legs in summer and tights and boots in colder months, and a waist tie or belt loops are worth having because a shirt dress with no shape at the middle can end up looking like you've borrowed your dad's shirt, which is fine for some people but not what most of us are going for. These dresses earn their keep in spring and early autumn especially, when you want something that looks dressed without feeling heavy, and they're just as happy at a lunch, a work thing where you need to look capable, or a Sunday where you're seeing people but not performing for anyone. In the shop, check the buttons sit properly across the chest without gaping, check there's a bit of give across the hips if the fabric is woven rather than stretchy, and have a proper look at the length when you're standing and when you sit down, because a dress that looks midi standing up can ride to somewhere unflattering the second you're in a chair.
Where this dress really pays off is how little else it needs. A pair of trainers and a denim jacket takes it casual, a pair of boots and a long cardigan takes it into fuller skirt weather, and if you belt it properly with a pair of heeled sandals it can do something close to smart without trying too hard. Layer a roll neck underneath in the cold and it still works, which is more than most dresses manage once the temperature drops. It plays well with things you already own rather than needing you to build a whole new outfit around it, which is really the whole point of a dress that started life as a shirt.
I'd start with a classic white or a soft blue chambray, something you can wear with absolutely anything else in the wardrobe while you work out whether you want more colourful versions later.