Personally, I think you have too many links on that page (>60). I’d try to split it into subpages, each one with no more than 20 links.
Although it’s tempting to allow webmasters to dictate what anchor text you use for their link, you quickly end up with a lot of generic-sounding links. For example, you have 6 ‘Online Casino’ links, none of which are actually online casinos!
Think of what that page offers to your visitors. Your Casinomeister link for example just says ‘online casino’ – no description, no site title, no way of anyone knowing what that link is all about. Try to persuade webmasters to allow you to write your own descriptions. If you do it in a way that presents their site well, very few will object. And those that do? You don’t need the backlink that badly!
Another aspect of using a set text is that you can run into duplicate content issues. Even if webmasters insist on you using a certain script, you can always add some text of your own to make it unique.
One final point – your ‘Partners’ page is there purely to get backlinks (ie it’s not really for your visitors’ benefit) Unless your link partners object to it being PR0, why worry? As time goes on and your home page gets more PR, you can start to be more selective about who you really want to partner with. My advice on that is to only exchange with people you have already formed a relationship with – ones you keep in contact with and can trust. You’ll know who they are! Good luck…