Looking for a rental unit for one month in HCMC

Try Ruby Star Hotel, 43 Truong Dinh St., Dist 3, between Nguyen Thi Minh Khai and Vo Van Tan.  It's about a 10-12 minute walk to Ben Thanh Market, through Tao Dan Park.  See Ms. Nhi or Mr. Chanh, depending on what time of day you get there.  They're reasonable, clean, and no nonsense.

Sorry, I should have added that I stay there for three months every year, sometimes twice a year, and have been doing so since 2011.  I've never had anything taken from my room, there's restaurants all over, and there's a good medical clinic right across the street.

There are many great, safe, serviced, small budget hotels in the Pham Ngu Lao area 5-10 mins from the Ben Thanh market area. $20/night +/- $5. Be advised though, it's mostly a backpackers area and, in my opinion, the main concern is that it CAN be loud with late-night bars & pubs. That's the only slight downside of the PNL area. But it can be a good area just to settle in for a few days, or week, and get oriented.

Cross the park towards the New World Saigon Center area - Ly Tu Trong Street, Cach Mang Thang Streets, Culture Park, etc. - and you will find safer, quieter, full-serviced apartments, with kitchenettes, etc in the $300-$500 range. There are mostly off the main streets (so, in the back alleys) but are very safe areas. Lots of food stores, cafes, etc. around.

It really depends on what you intend to do here for 1 month.
If you need help (from a fellow Canuck), feel free to connect offline.
Good Luck ...

Nice to meet you ? how much can you pay for your rental? I can look for you !

Just curious, but in your other thread on reclaiming citizenship, you stated that you were born in Haiphong.  As the first item you need to seek is your birth certificate, wouldn't it be more fruitful to base yourself there or in Hanoi?  Your photo makes you look way too young to have fled to Saigon from the North in '54.    If as you state you are on a budget, wouldn't being closer to where you need to do business be helpful?