Always negotiate your compensation in gross. Always negotiate hourly in hours, salary in years or months (most places prefer the former, but depending on your country it might be customary to discuss in the latter). A multiplication/division by 12 is usually sufficient.
Hourly pay means you work time, you get paid for exactly that time (give or take 15 minutes sometimes, usually it's rounded, often up to the next hour). Payments usually made every two weeks or every month.
Salaries are paid at a fixed frequency, usually monthly - sometimes, in very very rare cases, semiannually or even annually. Don't bother asking for a different pay schedule as it's generally company-wide and very difficult to change, and it also shouldn't affect you if you manage your own money correctly - the amount of money you make on average over time remains the same.
The reason for gross is, as you mention, taxes. Your specific situation affects how much you contribute to your community/country (via taxes), and the percentage/amount usually changes over time as your living situation changes (you get married, have children, get a raise, etc).
Your employer can't possibly know all of this in most cases (namely in the US, but also elsewhere) and also it's not their burden to manage your taxes (again, usually - namely in the US).
Your job is "I do services, you pay me for those services". The company needs to know how much they're paying for your services. How that income breaks down for you is your own deal.
Imagine a case where you're in a high tax bracket because you have a lot of successful side gigs. Your employer, paying net, would thus have to pay you more in order to keep the rate competitive for you, simply because you make more elsewhere. The employer loses out pretty heavily in this case. Just doesn't make much sense to do it that way.