I have BP51s with 2723s, SPC UCAs. I got the from OK4WD, who also does installs. A few notes:
1) I left the compression and rebound stock
2) even with a SLEE rear bumper, drawer kit, and recovery gear and tools, still have a slight rake in the rear
3) I suggest buying the BP-51s from someone who also does installs, even if you are installing yourself, as they can tell you if you'll need UCAs. Mine said yes (and they threw them in for free as I also bought an ARB bumper and other gear at the same time, and they were already having a sale - so they would have saved money if I didn't need them).
4) I'm pretty sure you need them - but there are at least a dozen guys on this forum that are way better at this type of stuff than me
5) I'm dumb enough to try to install them myself. If you aren't a good mechanic, I suggest at least finding a buddy who is if you are determined to do the work yourself. Even being careful, we messed up a boot on the CV axle, so I got to buy another of those on short notice. And, I just spent, 20,000 miles later, $1700 to get 2 new CV axles, Toyota brand, professionally installed - whatever we did, we likely reinstalled them (had to take them out to get new suspension and UCAs on) in such a way that we didn't perfectly get them back in. OR, the geometry is aggressive enough that you'll wear CVs faster than you'd like. I've done some wheeling with my 200, but not enough that I thought I'd be replacing them by now.
6) Not sure what tires you are going with, but without some lift, you are likely not going to be able to get a tire in there that looks proportional to the rest of the vehicle (that obviously my opinion, but I've always thought the LC200 looks silly with stock wheel diameter). I have the KO2s that are 33.8", and I still wish I could fit 35s.
If I was going to do it over again, especially if I didn't want lift, I'd go with Nitrochargers, which cost much less, don't require (I think) UCAs, and from what I hear, still make the vehicle drive much better. Surprisingly, I haven't competed in a Baja race like I dreamed of, so the BP51s just aren't necessary.