Adjusting a Remington 700 trigger is not brain surgery. There are limits than can cause serious safety issues so follow the factory procedure. The factory trigger assembly is not intended to be a target grade trigger, however the trigger pull can be greatly improved from the typical factory settings. Reducing the trigger pull does not reduce gritty feel, in fact it can make the trigger feel more gritty.
The top screw adjusts over travel. The bottom front screw adjusts sear tension. The back screw adjusts sear engagement.
The procedure is simple. Start with the back screw and adjust it so the sear overlaps by .030". You can look into the inspection hole while releasing and resetting the bolt. Usually the factory setting will be just fine. Less sear engagement is very unsafe.
Next, adjust the top screw so the trigger pull will release the sear completely and have a few thousandths of over travel. Cock the bolt and dry fire while watching sear travel in the inspection hole. Again, the factory setting is usually right on.
Last, adjust the lower front screw for trigger tension. Here's where the factory setting will be tighter than it needs to be. There is a fairly strong coil spring under the adjustment screw. If you back the screw out too far, there won't be enough tension to safely hold the sear. I've found 3.5 to 4 lbs is the lowest safe trigger pull you can get without changing springs or polishing internal parts. Actually, a 4 lb pull feels pretty good compared to the factory pull of 6~8 lbs. Make sure you capture the screws with finger nail polish or model airplane cement if you disturb the factory glue.
If 4 lbs isn't good enough, you should have a gunsmith take the assembly apart and polish all the friction points, then replace the sear tension spring. A better option for do-it-yourselfers is to install a Timeny trigger assembly. They come pre-polished, have lighter springs, and are safely adjustable from 1.5 to 4 lbs with little or no creep. (Brownell's P/N 883-400-270). Of course they aren't cheap, about $100, but a gunsmith would probably charge you that much to rework the factory trigger. Timeny includes a good set of instructions for installation and adjustment.