I am quite inexperienced compared to the most that commented, but I’d like to echo the advice many experienced riders here shared with you.
Get a bike fit and then aim for a used bike. I don’t know where you’re located, but I recommend you search your local bike forums/mailing lists for reputed bike fitters. In my area there’s at least one fitter that provides “pre-fit” where he talks to you about your riding goals, checks your flexibility (suggests stretching exercises based on your goals as well) gets you on a stationary fitting bike, determines a good fit based on your goals/current flexibility. He then recommends frame sizes, frame types based on what’s on the market. He then gives you 6 months to get a bike and works on your “final fit”, all included in your “pre-fit” pricing. If you go longer than 6 months to get your “final fit”, he charges a discounted rate on your final fit on top of the pre fit. It costs just south of $300, but money well spent if you’re a beginner and don’t know much about fitting and your capabilities.
That way, you’d know exactly what parameters you need to stay within when you’re shopping for a used bike, and I’d bet you’d still spend less than a new bike on what you spend on fit+Used bike combined.