There are different versions of Rem 700s. You must have had a varmint or target barrel version.
Stay away from the Rem 783. Of all the budget priced rifles it has the worst reputation. With ANY of the budget priced guns these days its not accuracy thats the question (they are all accurate) its the build quality and workmanship. How smooth is the bolt? What are the components made of? What is the finish like? Things of that nature.
You might be confusing the 710/770 with the 783...those 2 are pretty terrible examples.
783 is pretty decent in the $400-$500 range, no real issues with them, decent enough trigger, well made, syn stock is not butter container quality, and they are pretty accurate. Molded in sling swivels are the only possible negative, mine still haven't let go. If they ever did, it's not hard to clean up and install a metal sling stud.
The walnut ones are nicer stocks, but should be compared to the syn stock prices and decide if the difference is really worth it.