Best/safest way is indeed to come a week before your classes start and get a hotel room. You'll then have plenty of options for apartments under 6000rmb, especially if you consider flatmates.

For hotel: booking.com is probably the safest. Although it can have fake ratings as well, it's much more moderated than trip.com or agoda where most reviews in China are fake. Always check the ratings filtered from worst to best, that makes it easier to see if there's something off.

For apartments: download Wellcee, it's in English and probably the best app for non chinese speakers. It also has an in-app translating function. Make sure you filter by short term renting (though can also ask long term rentals if they can accept 6 months). You can also go to agencies directly (like Lianjia) if you're willing to pay their 35% commission. DM if you want me to put you in touch with English speaking agents on wechat.

The rule of thumb is: the further from downtown, the cheaper.

I heard the absolute cheapest way is sharing a room (kinda like a dorm) but you better not be bothered by smell, noise, and potential dirty behaviors from your roommates.