Tracy,
I'm not sure if your were interested in a 3rd party backhoe such as Woods etc. or a John Deere backhoe? There are two John Deere models that will fit the 4300, the 47 hoe and the 48 hoe. The 47 is smaller and less capable, but comes in around $1000 less than the 48 hoe. I just purchased a JD 4310 with a 48 hoe as I thought I got a lot more performance for not too much more money.
Either JD hoe will do the job (47 has 7.5ft. digging depth and 48 has 8.5ft. digging depth), but the 48 will be faster.
As for 3rd party hoes... I guess comes down to a question of money and convenience. The 3rd party hoe may be cheaper than the JD hoes, but then you get into problems of fit and convenience. The JD hoes are designed to go on and off in less than 5 minutes without leaving the tractor seat or picking up a tool.
I bought JD brand implements where I felt the fit/convenience was more than worth the extra $$$. When it comes to things which go on the 3pth, like a box blade, I will buy 3rd party because that stuff is more or less standard and less $$$ than Deere for the same or better quality. 3pth implements are pretty much standard and fit isn't as much of an issue. When it comes to loaders, hoes or implements that run off a mid PTO like the MMM or front-mounted snowblower, I think the extra $$$ is worth the headaches/time saved down the road when you change implements between jobs and need stuff to just work.
If money is the overridding factor, then the 3rd party hoe might be your best option as long as you understand the potential issues going forward and make absolutely sure that the hoe is designed to work with that tractor. I'm sure there are other 4300 or 4310 owners here that have 3rd party hoes and would be more than willing to share their experiences so far, both good and bad.
One last thing that caught my eye in your post was the mention that you were looking for a hoe without stabilizers. I don't think I've ever seen a hoe without them. Pardon me if I misunderstood your wording and I don't want to come across as lecturing, but I think safety is the first order of business when working around tractors and their implements.
Too often people sacrifice saftey for convenience. They remove guards, adjust PTO equipment off the tractor while the PTO is runnning, don't use ROPS etc... Just take a look at the safety forum on TBN and the horrific accidents that are talked about there.
I wouldn't want anyone to get a piece of equipment without the proper saftey features in place. The stabilizers are a safety feature if nothing else. Unless there is some exotic circumstance that I've never heard of, I wouldn't think that anyone would make or sell a hoe without stabilizers or another stability compensating device. Just the thought of lawsuits should shelve that idea before it ever gets to the drawing board.
Well, enough of that, I'm sure you get the point. I'm sure some other folks here will be lending their friendly advice and hopefully you'll soon be armed with enough knowledged to move on to that 3rd stage and buy the hoe so that all important 4th stage can be enjoyed - simply using it. /w3tcompact/icons/smile.gif Good luck!
Sleepyhollow