Bullet suggestions for my new .243

[Cossack]

Do check the twist rate and purchase you bullets accordingly: 1 turn in ten inches will benefit from a heavier (longer) bullet like a 100gr.
But if its a 1-12, like some Remingtons from that time frame were, then a lighter bullet like 70 to 80 griner will likely shoot more accurately. And yes, do try several brands to see which it shoots best.
To measure twist: Insert a cleaning rod with brush and patch into back of the action until it starts to turn. Mark the rod with a felt tip marker where it is even with the back of the action (mark 1). Without moving the rod, make another mark closer to the handle. This one should be along the horizontal axis of the rod, narrow and about an inch long, so you can tell when the rod has turned one complete revolution. Now, push the rod in until it's turned one full revolution. Mark the rod close to action like you did for Mark 1. (we'll call this mark 2)
Now pull the rod out and measure between mark 1 and 2 .