To answer the first part, when you shutdown the VM, your stuff will persist, so no you will not have to reinstalled all your stuff on the VM every time.
For the second part of your question, (to my knowledge, please correct me if I'm wrong) no Mobo has a built in GPU, some CPUs have integrated graphics and I believe you can get that to work on the VM as well. Otherwise you could use integrated on the Linux host OS and use your GPU for the VM exclusively, but your overall performance may take a hit when not using the VM
To answer the first part, when you shutdown the VM, your stuff will persist, so no you will not have to reinstalled all your stuff on the VM every time.
For the second part of your question, (to my knowledge, please correct me if I'm wrong) no Mobo has a built in GPU, some CPUs have integrated graphics and I believe you can get that to work on the VM as well. Otherwise you could use integrated on the Linux host OS and use your GPU for the VM exclusively, but your overall performance may take a hit when not using the VM