There are pros and cons for either, of course.
Having own server requires having someone who can maintain it, that is someone who licked some php and mysql
and is familiar with either windows, osx, or linux (whatever you would run your server on) at admin level. Your "Mac" photo implies you guys have Macs around which make serving easier.
Having own server affords you customizing, tweaking, and patching Moodle as you wish or require, and using the version of Moodle that you want.
Having your own server must not mean purchasing new hardware. A hand-down computer might be fine to get you going. If it can't handle the load, you split service onto two computers or get a better one.
With 35 courses and 1000 students, you do not have that high requirements IMHO
, so either solution will be fine. You can check the "servers and performance" forum where those things are discussed widely.
We are using the 1st generation G4 with OSX 10.3.9 with ram upgraded to 1 GB for 24 courses, 350 users. No sweat. Next semester we will have 120 courses and 1600-2000 users. I plan to swap the IDE drive for fast scsi drive and up ram to 2 GG when the server starts bogging down, switching to G5 later on if load keeps going up. But it will be a while before all teachers take full advantage of Moodle.
On the other hand, using service provider, particularly a Moodle partner, frees you from those technical issues. You just need to budget paying for the service.