Need some advice to find records with proper fields values

It depends what you want to achieve (render the result, or just get a record list). If you want to display a list of records, you can use a pre-filtered link (like you mentioned) already. Another way to do it, is the "Render an article list" through an api call. See documentation here.

To get a list of matching ID's, i would query the #js_res_record_values table based on the field_key and field_value. This query will be much faster than querying the #_js_res_record with a "LIKE" statement.

Example of what Sackgesicht is suggesting may be like this

SELECT id, title FROM #__js_res_record 
 WHEER id IN(
    SELECT record_id FROM #__js_res_record_values
     WHERE field_value = '{$name}'
 );

Thanks, it's great:) Somehow i didn't noticed the #__js_res_record_values table.