Ok! There is no reason why you can't apply for primary with a history degree, it is a primary subject too!
Routes: PGCE, primary or secondary, advantage that the course is likely to well established and you will be able to find out how others found it fairly easily. Perhaps easier to get on than school based course (but that depends where you are)
School based:
school direct, basically the same course as PGCE but more time in school and some or all of the academic stuff provided by a university partner. Course administered by a teaching school where you may train or they may provide quality assurance for the school where you do train. Advantages: moe immediately hands on, you "belong" more in your host school and still have the background support of a university. But disadvantages: some schools are not as good at this as they should be and it is harder to know how to resolve issues (although still possible)
SCITT: school based but school provides all the training (normally at the teaching school managing the cluster) programme is accredited by a university but not administered by them so the schools devise their own. Can be very good but very dependent on individual schools. Disadvantage, they haven't been around that long in their current incarnation so hard to find out much about what they are like.
Salaried: as you identify you would need to have worked in education for a while to really get a look in and even then it is by no means guaranteed. There are not a lot of these places and their future is not certain so you could work as a ta only to find the government no longer considers them "cost effective"
Most primary routes are very competitive so you will need lots of experience. It is probably a bit easier to access PGCE than others but I would apply for a range. Consider also if there is a school direct provider slightly off the beaten track. I say this as someone who runs a school direct programme in a small town very near a big city - we get far fewer applicants than the city although our course is good and accredited by the same university.
Feel free to pm me if you want to ask anything.