One that will work on both the PC and Mac and fit in your budget is Adobe Premiere Elements (14 is the latest release). Retail is $69.99. You may be able to install it on two computers provided you don't use them both at the same time and if it comes with install media for both the Mac and PC. Check section 2.1.3 of the license agreement. Here's a link to the system requirements:
https
/helpx.adobe.com/premiere-elements/system-requirements.html
Here are some others but I can't comment on how good they are:
VideoPad Video Editor (NCH Software)
muvee Reveal Finale (muvee)
I'll give adobe a try. thanks Also thanks awesomeaiden for your input too
Open Source and Free Software:
VideoLAN Movie Creator (free from videolan.org)
Shotcut (shotcut.org)
Most, if not all, have trial versions available.