Hi,
I have been developing websites with Joomla since 2008. I have also performed a number of upgrades in the last few months and I know what it takes to migrate. You might not be aware of this but there are no reliable automated tools to upgrade from 1.5. Using them usually ends up with a half converted site with a lot of problems that can be tricky to fix. That's most likely what you will get for a low budget. My experience is that it's actually saving time to start with a fresh install of Joomla 3.2 and check all the extensions, some may not be available and require a replacement, then transfer user groups, users, categories, articles, menus and extension specific content in that order.
I then redesign the template, keeping the look and feel of your old site if you so desire but using protostar, the Joomla 3.2 responsive default template as a base. This way you inherit responsiveness and your site is mobile ready.
It would be helpful to have the list of extensions and your site url.
Do not hesitate to contact me if you have any questions.
I'm US based which could make communication easier.
I look forward to hearing from you.
Regards.
Xav.