Can I run a Test Installation? If so, how?
I would add a few more specifics to petednz's answer, because we were in exactly the same boat a year ago. I got a free non-profit (we are the San Diego County Bike Coalition) account on Dreamhost, where I installed both Wordpress (clone of our mature website) and the latest (at that time) version of CiviCRM. This is a shared hosting account and NOT recommended for your final deployment, but it sure was a good test platform for us. If you want something more local, I also set up XAMPP environments on both a linux and windows laptop. XAMPP gives you a local Apache web server, PHP, MySQL (MariaDB), all on your laptop or desktop. That way I really couldn't break anything. Both these environments, temporary hosted website or local XAMPP website, are definitely DIY. If those are foreign to you, a CiviCRM partner would be recommended. 

Having an actual hosting site like Dreamhost for the initial setup and test period was crucial if you have multiple people working on it, as you each need to have access to the evolving configuration through a browser. Now that we are fully hosted on a VPS, I still rely heavily on my local XAMPP instance(s) to test out new things and also to run updates locally first, as updating either Wordpress or CiviCRM always has the potential to zap your website. Realize that a local desktop/laptop setup, though, is only useful for ONE person.

I might add that it is quite easy to migrate/move your test configuration into a different location or different server. We follow religiously the steps at https://wiki.civicrm.org/confluence/display/CRMDOC/Moving+an+Existing+Installation+to+a+New+Server+or+Location.

I think you will love CiviCRM. We are amazed, nearly daily, at all the functionality it provides. By taking care of the administration on our own, we have saved the SD County Bike Coalition at least $5,000 annually by dropping commercial packages for contact database, transactions, mail management, event management, which all had monthly or annual fees and didn't integrate well together. The real savings, though not easily measurable but way more than the $5K material savings, was in eliminating staff time and frustration having to learn 4 different applications and constantly dealing with manual intervention because they were so poorly integrated. If your organization fully embraces it, don't forget to contribute to CiviCRM, because it does need to be supported to be sustainable.