How long it takes to let depends on a number of factors. Some you can’t change like the location. Others you can, like the condition, price and furnished v unfurnished.
A good agent with local knowledge should be able to advise you on all these. But it’s really specific to each area, which is why local is best.
You can look on Rightmove and adjust the search function to include “ let agreed “ . That way you can see what’s available and what’s gone already. I’d set up some alerts then check them every day. Save anything that’s like yours and / or near yours to your favourites.
You can make notes that only you can see - note when they come onto the market ( it’s on the listing ) and when they are let. Make a note if anything is reduced as the old price will disappear.
If you have saved it to your favourites it will stay there even when the listing is removed by the agent ( they usually do this as soon as a let is agreed so they don’t keep getting enquires ) .
Start today and you will soon see a pattern. If you don’t know the area well you need to look up each house on Google maps, so you can check out the location. Otherwise you might not understand why one is cheaper / dearer than another .
Remember it’s better to spend, say £500 doing repairs / redec than have the property on the market for a month longer ( assuming your rent is more than £550 a month ).
You will need to pay tax on the whole rental income , minus costs like repairs, replacement furniture, insurance and agents fees. You can’t deduct improvements, buying furniture for the first time and your mortgage .