If your budget is only sgd800-1000, honestly the choice is very limited to you. Coz the cheapest choice should be Hdb room. Hdb 1 room (share toilet) is about 800-1000 if near city and master room with city can be 1200 or more.
Safey should not be an issue, just need to tell agent you want to rent room with other Female only. Before I married in Singapore, I also rent room and share with other HK girls.
I started worked and rent room in singapore. Now have stayed here for 5yrs and got 2 kids