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There are many ways to autoselect purpose or any other field, one most simple version is with custom url on page with search/results like:
Check also this from docs may be helpfully:
https://wpdirectorykit.com/wp/show-properties-for-rent-sale-only-on-specific-page/
There are also custom coding ways with custom javascript and similar on very special cases.
If you need some special case please contact us via our website contact form.
You are welcome!