Any of the 308 based cartridges will be good. The 308, itself, is always a very good choice for a practice rifle and is also a very respectable hunting cartridge with extreme accuracy potential. If you decide to do a little competitive shooting for practice it is still a good choice. My son has made several kills with a Rem 40X F-class rifle in 308.
Home For Thanksgiving
The rifle is a little heavy for hunting but the accuracy makes up for that.
Nothing wrong with the 7-08 if that is what is available. Main job is to get the practice and it dos not matter a whole lot how you get it.