I assume that you want to use the rifle's magazine. One of the first things that I would want to know is the throat length of the chamber. To measure this, I would suggest that you purchase a seating depth measuring tool that Hornady makes. Another of their tools that you should have is what I think that they refer to as a headspace tool. This will be useful for setting the amount of shoulder bump that your FL or body die gives, as well as allowing you to measure a fired case, so that you can compare its shoulder to head dimension to that of the case that you bought to go with the seating depth gauge, to come up with a correction factor. While you are at it, you will probably want an their tool that is used to measure loaded round length off of bullets' ogives, rather than their tips (meplats). For trimming, I would recommend a Wilson trimmer, and the appropriate case holder. You may also want a trimmer base, to raise the trimmer and make it easier to clamp to your bench. Since Lapua brass has such concentric necks, I would do my first load testing with unturned necks. New brass can have too much neck tension, at least in some calibers, so you may want to buy a expander die and mandrel. (Be sure to use lube when you expand, and remove it afterwords.) I would buy the brand that corresponds to the turner that you might wish to purchase, if you decide to go that route. On that subject, I would stay away from turners that are trimmer attachments, and make sure that which ever you choose has a carbide mandrel. Since we don''t know your magazine or throat length, it is difficult to make suggestions about where to start on seating depth, but if you come back with that information, I am sure that some good advice will be forthcoming. Just be sure to give loaded round lengths to the tip of bullets for this part of the project. When I record data, I give both (to tip and from ogive). For setting dies, I use the length from the ogive, because it is more precise. I prefer to start with a seating depth that experience tells me is likely to produce good results, but since that has usually been .006 to .010 longer than touching, and it is likely that your Remington's throat is too long to reach, with bullets seated to magazine length, I am a loss for a starting length. I am sure that others, who have experience with rifles like yours can be more helpful. In any case, I would first do a mini ladder test, starting with a powder that is seems to be popular for your particular bullet and caliber. Back in the day, when I was shooting 168s and 190s in my first CF rifle, a 788 in .308, that powder would have been IMR 4064. These days I would probably try Varget to start, since it is usually easy to come by locally, and do some research on what Vitavuori would be in the same burning range, because I have had such a good experience shooting 133 in my 6PPC, as far as accuracy and level of fouling. There is a long list in the burning rate range that you will be using, and a number that have given one shooter or another with good results. When I shot my combination ladder/pressure test, I would be loading at the range, and initially step my loads by .4 grain, starting in about the middle of the range in a reloading manual, going up till I saw pressure signs, or ran out of room in the case. For this test, I shoot one shot per load, over flags, shooting carefully, from a good rest setup, on the same target, keeping track of where each shot goes. When it is over, I look at the target for any groupings that might indicate a good load range, and load three test rounds with a powder charge in the middle of that range of weights. If that looks promising, I may use that powder weight and start to play around with seating depth, initially with only two shots per setting. If I were trying different amounts of jump, I would probably try longer increments as the jump became greater, to a limit of .005 per change. Once I came up with something that looked promising, I would refine it with smaller adjustments.
One thing that I would consider adding to your rifle is a Jewel trigger. I think that you will really like it. If that is not in your budget I would suggest a spring set for your factory trigger from erniethegunsmith.com.
Shooting small with rifles that kick as much as a .308, loaded with heavy match bullets, requires a different technique than a varmint rifle. It is easy to think that you have a load problem when when the problem is how you are shooting the rifle. Many times I have been able to cut shooters' groups in half, with changes in how the rifle is supported, and held, how the trigger is pulled, and making them aware of the importance of good follow through. I also find that most shooters don't really understand what parallax is, and how to properly adjust their scopes. The reason that I bring this up is that it is easy to fall into the trap of trying to fix everything with load changes.
Above all, have a good time with your new rifle, an don't forget your eye protection. You only get two.
Boyd Allen