Rem 700 is a good starting point, but hey... SAKO is better. The rest depends on your defenition of precision shooting.
The 223 is great, again... for what?
If you want to shoot 600 yards plus then you will need an 8 inch barrel twist so you can shoot 80 grainers, or maybe a 6.5 twist so you can shoot 90 grainers.
If you just want to plug ground hogs at 200 yards with 50 grainers, thats different.
The trigger is not critical to field gun accuracy. Focus on the barrel weight and twist rate. BUT to answer your question... Yes it will accept jewel, timney CG triggers with no problems.
If the barrel on the rifle you mentioned has a 13 inch twist rate, it will not work well at 500 + yards, and not great at 300.