it depends on your life style as well. from a perspective of a young lady, if i were in your shoes i would definitely change it had it been over 20 years. (you mentioned there are only 1.5 bath in your home in the post prior, right?) life would be much easier as you wouldn't be trapped into limited shabby bathroom. no offends here, just thinking from as being a wife and a mom.
Replacing a old tub with a new one is a big job, equivalent to redo the whole bathroom (even harder than building a new one). The standard cost to build a small, brand-new bathroom is $3,000. You need to tear off all ceramics, tear off the dry walls, since most pipelines are hiding inside the dry wall. Then, put them back after install the new tub. I suggest you to get an estimation by a professional (know how much you might need to spend, usually the estimation is free) before making a decision. Good luck!
I saw some flyer saying you can just cover new arcylic layer on top of your existing tub, so it looks just like new. They claim that it will be cheaper than replacing and they will do it the same day for you. You might want to lookup the local flyer and call to check out.
You can buy some bathtub cleaner from walmart, spray them on, wait 5 minutes and use a brush to clean it. If you feel "个应" use bleach to disinfected it.