It took 9 months for us to be approved and apparently this is quick!
If you are in Enlandandwales, it's not.
Exactly what happens in stage 1 and 2 varies by agency. Stage one is loosely made up of information gathering- having to do a big workbook is typical, though this often leads to repeating the same info in stage 2. Training usually occurs towards the end of stage one or start of stage 2, but can occur at any point (we did ours when almost finished).
The whole process should take 6 months from ROI to approval.
Despite the many posters who will tell you it was much longer for them, it really should take this long in most cases.
The most common (valid) reasons for delay are: further medical reports needed, work history abroad needs chasing, adopters choosing to pause or complex issues from prior partners need investigating. So it is entirely normal that it might take more than 6 months, but only for a reason.
In practice some agencies (often, but not always LAs) don't have the staff to do the work or don't have efficient systems for performing checks. So every staff absence and every extra check creates a delay. I know of an LA where almost every application ran over for years because they sent out the medical questionnaire (perhaps the most common cause of delays) towards the end of stage 2! They got round the statutory target by massaging figures.
@OP Stage 1 should not take 3 months without a reason. Ask.
Learn not to stress about timings, and you will go a long way.
If we'd done this it would have delayed DD2's placement by months. If you like to be laid back, then by all means be so; but this is the process by which you have children- ask as many questions as you feel comfortable with. There are certainly likely to be times when dealing with SW where you will need to be a little pushy to get a good outcome.