<input type="submit" value="Next >" name="nx">

Unfortunately that means altering the query doesn't restart at the beginning of the DB after hitting return but continuing where the last query stopped.

So it's necessary to click

New <input type="submit" value="Search" name="go">

explicitly.

I can't see an application for binding the return-key to "Next >" while it's handy after altering a form entry.¹

My suggestion would be to add a hidden

<input type="submit" value="Search" name="go" style="display:none">

prior to

<input type="submit" value="Next >" name="nx">

to change the default for return-key.

This SO discussion shows different ways to do so how-to-submit-a-form-when-the-return-key-is-pressed

I haven't tested yet...but I think we have enough HTML expertise in this board to find a solution! :)

¹) for creating a keyboard submit you need to select a form element. The only way to select "next >" w/o clicking is to hit the "tab"-key. But in that case pressing "bar"-key has still the effect to continue the search.

All other form elements should be bound to "Search" again.