If you use radio buttons, be sure to put them into an option group, otherwise you'll be able to select both. I was working on a db with a search form, but my intention was to have it much more robust than what you've shown. Alas, I got distracted by life (and maybe spending too much time here answering questions ) and haven't gotten back to it.
What you want can work, but it requires a lot of thought and coding. As June7 implies (I think) and/or can be tricky but if you are not trying to nest them, prevent unsuitable choices from being made and don't allow conflicts then I think they should work fine. Search forms might function better if combo's are used instead of text boxes for certain fields so that garbage can't go into the search. A name field is probably not a good one for that. Once you have the design, the hard part comes. You have to concatenate criteria if there's more than one possibility and deal with situations where the first is supplied, but not the second (or vice versa) to avoid getting no results. You might also code for the possibility that incorrect data types are entered.
Another method is to search as you type - filter the records displayed according to a search text box by using the OnChange event, but again, you'd have to concatenate the filter expression if it involves more than one field. That method allows the user to immediately see the result after each character is typed in since invalid criteria results in no records being displayed.
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.