There's going to be no 100% solid answer to your question since we don't have your home Internet connection and aren't at the same campsites you're at. But the factors will be:
- How fast is your home (or wherever the Slingbox will be located) upload speed? This will give a strong indication what downstream speed (at the campsite) you'd actually be able to use. If you can't push more than 1 mbps upload at home, it won't matter if the campsite has a 30 mbps download speed.
- How fast is the campsite's download speed (especially versus the WiFi devices in use at the campsite)? I was recently at a hotel in a tourist area with "high-speed WiFi" that gave 300 kbps download on the weekends (when the hotel was full) and a 3 mbps (i.e. 3000 kbps) download on the weekdays (when the hotel was 50% filled). I have 1 mbps upload at home, and my Slingbox 350 was unwatchable on the weekends and watchable on the weekdays.
Also somewhat related is how consistent the speeds are--for example, a consistent 1 mbps upload (from home) and 1 mbps download (at the campsite) will give you a much smoother experience than a consistent 1 mbps upload and a download that fluctuates between 300 kbps and 3 mbps minute-to-minute.
So the answer is a big, fat, "it depends".
It also depends on the content you will be watching. When there was nothing better available at reasonable cost, people put up with VHS quality for years. At 300 kbps, if it's stable, that's roughly what you'll get. For watching comedy or a talk show, IMO it's fine. However, if your interest is action sports, you won't be a happy camper.