Frankly, a budget of $500 seriously limits the choices. One of the facts of life is that small guns are just as expensive to design and build than full-size guns, perhaps more so because the small size makes details more critical to reliable function.
Another critical factor is your definition of "sub-compact". For example, we have a Glock 27 that Glock calls a sub-compact. Yet, it's a tank compared to my Kahr PM40 - longer, taller, wider and heavier - and considerably more challenging to conceal. Although more pleasant to shoot. This certainly applies to the Sig P250 that you mentioned.
Keeping your budget in mind, I'd suggest three guns:
1. Smith & Wesson M&P Shield 9: Unfortunately, current demand grossly exceeds supply. FYI, my wife picked up her Shield 9 yesterday and after a long afternoon at the range where we compared it back-to-back with a half-dozen other small CCW guns, the Shield became an instant favorite.
2. Kahr CM9 or CW9 - possibly problematic for a woman or small man to rack the slide. Can be solved by putting grip tape on the slide.
3. Ruger LC9 - no personal experience, however I have heard of complaints RE the slim grips being too slim to be comfortable to shoot. FWIW, that could reflect on the expectations and inexperience of the LC9 buyer.
Other things to note:
The smaller & lighter the gun, the more comfortable it is to carry. While some folks will attempt to persuade you that size & weight don't matter. Don't buy it - they do.
The smaller and lighter the gun, the less comfortable it is to shoot. Fancy recoil systems and differences in grip can make minor contributions to shooting comfort, but nothing beats mass for damping recoil. If this is going to be your only gun, then I'd suggest selecting something that pushes the larger/heavier end of the sub-compact genre. Otherwise, you probably avoid practicing.
Thin guns conceal much easier than thick guns. My wife is not petit and wears loose clothing appropriate to her status as a senior citizen. She can wear her Shield, Sig P938, Kahr PM9, S&W 3913LS or 4.25" 1911 and you can't tell she's armed. Strap a Glock 27 on her and the bulge is noticeable.
Extended mag base plates that give a full three-finger grip can bounce and pinch the flesh of the pinkie finger. :shout: The Glock 27 & Kahr CM9/PM9/PM40 are guilty of biting at least one of us - especially the Pearce grip on the Kahrs. OTOH, the M&P Shield, M&P Compact, Sig P238/P938, and S&W 3913LS have never pinched either of us.