Don't let the onsite/offsite thing get to you, I've done both and actually prefer offsite for the exact reasons you listed.
The Radisson is a good bet, usually a decent rate for somewhere a bit better than the standard hotel. There might be better deals to be had out there on accommodations, but at the risk of staying somewhere "questionable" and you don't want that on your first Disney Trip. If you do some sniffing around the Bronson Highway you might find cheaper, but I wouldn't stray from the chains and don't go lower than $75-79 a night.
Here's some tips I can make to keep your costs down while offsite:
1) When you arrive in the morning and pay for parking, keep your parking ticket for the day, don't toss it out. If you leave and come back, even to a different park you won't have to pay again - a single parking lot ticket is good for the day anywhere in WDW.
2) Try to eat both onsite and offsite. Offsite is generally much cheaper than onsite dinning, but don't deny yourself some of the unique dinning onsite. Here's how my family does a typical day: Arrive early, eat lunch in the parks, then around early to mid-afternoon (say 2-3pm) go back to the hotel for a break, have supper offsite and then return to a park that's open late. That's a great time to do World Showcase as it's always open to 9 pm. Saves a lot of money, and also can provide a bit more variety for your kids because WDW Kid's menus tend to be the same 4-5 items everywhere!
With a 8 and 5 yr old you'll want to do a Character meal - note breakfast ones are much cheaper than dinners. You should book this now if you haven't already with the Advance Dinning Reservations system on the WDW website. (Bonus dirty little secret here, if you book breakfast at a monorail hotel, you can park there for the day, get the monorail to MK and back, and you skip the parking fee that day) :lookaroun
Also for breakfast, I believe the Radisson has an in-room fridge and microwave. Find a grocery store and stock up on breakfast items, go out and enjoy yourselves when you want for breakfast, but eat some of them in your room. It not only saves money, but time. One of the best times to be at the parks is first thing in the morning (9-11 am) when crowds are usually a bit lighter. If you're not familiar with the Southeast US, Publix Supermarkets are your best bet for selection and pricing.
Other tips:
One perk you may hear about onsite is free delivery of your in-park purchases to your room instead of carrying them all day. What they don't usually tell you is offsite guests can get a similar perk. Any gifts you purchase in the park can be sent to the front gate or in the case of MK, the Transportation & Ticket Center, for free pickup when you leave that day.
EMH nights: If you can, avoid the park that has EMH on that night, it will be extra crowded that day. But if you do go to a park that has EMH, you don't have to leave when EMH kicks in. You just can't go on any rides, that's the only place they check for your room key. So you can still shop, eat, watch fireworks (if any are scheduled, Illuminations for example) and so on. If you do end up in a park on a EMH night, don't waste time shopping during the day, do it at night when the EMH kicks in. (another tip: the parks keep the shops near the front gate open a hour or so after the park closing time, so this time-saving tip pretty well applies every night!)
