Get adult swimming lessons from a good teacher. Avoid expensive 1 to 1 tuition and go for a small group session of 5-10 learners - no more.
Are you happy putting your head under water ? If so, you won't need arm bands or other unwieldy aids. A float ( kicking board ) will be enough. I would recommend goggles, too.
Your lessons should include confidence exercises and the all-important ' push and glide,' to, and away from, the wall, leading on to adding the leg kick, then arms, then breathing. Front and back.
The human body floats with very, very rare exceptions - only just ! and you have to gain confidence and allow the water to support you.
If you rely on the weekly lesson only, it could take several weeks to achieve your first width , but if you practice between lessons ( 3-4 times) you will make much faster progress.
Good luck. You should enjoy it immensely if you are taught properly.
PS. I was a professional swimming teacher for many years ( ILEA, schools etc) and an ASA National Coach.