This is what I recently bought for a particular task at work. Overall, I'm pretty impressed with it. It fits very nicely in my hand, feels very durable, and has plenty of power for a 12 volt tool. It is pushing the limits of your budget.
Our maintenance shop converted from Dewalt to Milwaukee power tools a few years ago and the techs are very happy with the new tools, including drills, drivers, impacts, handheld band saws, heat guns, etc. A few of us at work have also started using Milwaukee at home. These are very good tools. the drill I bought is only my second experience with Milwaukee 12v tools, the first being a 3/8" ratchet. Both are very good tools.
https://www.homedepot.com/p/Milwaukee-M1...07-22/204300706
Another option that you may consider is the Rigid. I have no experience with Rigid power tools, but there have been a lot of very good reviews here on BITOG. Why I recommend it is because of the lifetime warranty that includes even the batteries. You just have to register the warranty to get the lifetime. If you fail to register it, it is a 3 year warranty.
With the lifetime warranty, you will never need to worry about the expense of replacing batteries. For casual home use, this may be a great choice for you.
https://www.homedepot.com/p/12-Volt-Lithium-Ion-3-8-in-Cordless-2-Speed-Drill-Kit-R82005K/205754094
I don't know if you can even buy NiCad drills any longer, but you wouldn't want to. Brushless would be nice if you were using the drill as a professional, but for casual home use you don't need it.