You can buy a used Savage dirt cheap. They are very common on the used gun market, and you can always sell it if you don't like it (or when it is time for an upgrade). Any decent 3x9x40 scope will do the job, but it would make sense to set aside a fair portion of the budget to get the best available.
Some people like the accutrigger, some do not.
The .243 Winchester cartridge would be a good compromise for your list of purposes, and ammo is found easily.