As a first horse, stay clear of any babies (anything 5 and under, unbacked or less than a year or two under saddle). Tempermant is key - I'd recommend something level headed and dependable if you're still learning yourself (I'm not sure what experience you have but steady and dependable always makes for a happy life if it's your only horse). Observe how they act and react when viewing and trying out - you can learn a lot about their personality on the ground if you have a sharp eye. Don't skip the vet check - soundness and decent health (that won't cost an extra horse to manage ) will save you a lot of trouble in the long run. Best of luck!
Bring someone trusted and experienced with you! Get any horse you are strongly considering buying vet checked. Ask for a trial period (even at owners yard, a lot don't give horses out for trial anymore).
Be patient! I got so fed up looking at horse after horse for months, that I almost rushed into buying one that didn’t suit me. I’m so glad I waited and i found exactly what I was looking for!