No problem

I would say not to pick private accommodation because they are likely to ask you for a deposit and in these uncertain times, it might be best not to go for something like that? Up to you though!
If you want to go with the University of Southampton halls of residence, you can pick from places such as Glen Eyre, Highfield Hall, Mayflower, City Gateway, Archer's Road and Wessex Lane halls of residence.
Glen Eyre is really close to highfield campus if you're going to be there a lot. Highfield hall is very close to avenue campus as well. Mayflower hall and Archer's Road are closer to the city centre if you like lots of nightlife and things like that. It's also near to the train station if you're planning to commute a lot. Wessex Lane, Highfield and Glen Eyre are in really nice areas, low crime, residential and quiet. I should not that Archer's road is also very residential and is nearby the largest greenspace in southampton - the southampton common.
You're guaranteed University accommodation if you apply before the 1st August 2020 but only if you're a non-EU new postgraduate student.
You will not have to pay anything until you receive an offer of accommodation from the University of Southampton accommodation team. Because you are a postgraduate student, if you accept the offer, you secure your place by then paying £350. THIS IS NOT A DEPOSIT. This is just an amount taken from the total amount for your contract.
I hope this gives you some insight, if you have any further questions, quote me with them and I'll try my best to help!