How should I plan my return flight if I want to extend my stay in Thailand beyond 60 days?

Looking for some advice, please.

Am a UK citizen planning a 3 month (90 day) stay in Thailand.

I understand I should benefit from 60 day visa exempt stay on arrival and may then be allowed to extend for a further 30 days.

If so and in which case, when should I attend at the Immigration (or whatever) office for my bolt-on 30 days because, assuming the extension is granted, does the additional 30 day period commence on the day it is approved or is it counted from the last day of my 60 day visa exempt period?

For example, if I arrived on April 1st, what would be the last day in June beyond which I would be classed as having overstayed if I attended at the office, say, 3 days before my 60 day period was up?

The Time and Date website calculates that 90 days from 1st April would be 29th June (including both the 1st April and 29th June in its calculation).

Effectively, if intending to arrive on 1stApril, should I book a return flight for 29th June when booking my flights or would that mean I would have to apply for an extension on the very final day of my initial 60 day exemption?

What I don't want to happen is book my return date and find it causes an overstay I have to either pay a fine for (as well as receive a blot on my passport) or pay for an expensive flight adjustment.

Hope that’s clear enough but would welcome any questions so as to help clarify.

Many thanks.