John,
If you really MUST neck-size, the Lee Collet type is a good choice. Very quick to use, no lube needed etc. I loaded thousands of very good cartridges using a cheap Lee Hand Press and collet dies in .243 Win, .308 Win, 6.5X55mm and even .300 H&H Mag at one time - last named just fitted the Hand Press! You can do your sizing in an armchair while watching the telly too! I don't think today's collets are nearly as well made as early models though and often have bits of metal in the gaps in the collet tines. They can be a b*gger to disassemble these days too while early models saw the collet section push out with a bit of finger pressure.
It's a myth however that neck-sizing gives more accuracy in a typical (read factory) chamber. In fact, it often gives poorer accuracy because the chamber is neither perfectly concentric nor perfectly aligned with the bore.
So I'd stick with the FL die if I were you. BUT ..... take a lot of care on headspace. Many people push the shoulder too far back using standard dies setting them up in the default mode with the die body in hard contact with the shellholder and press under tension. That may be exactly right for your chamber or you may set the shoulder back too far by several thou' shortening brass life. You can do this by disassembling your bolt and removing the mainspring / striker / cocking piece assembly using the body only (Essential!). Set the FLS die up as normal in the press - remove the decap / expand stem to avoid overworking the case - and then back it out from the default position by say a turn and a half. Lube and size a case and try chambering it in the rifle. It shouldn't go in as the shoulder will be too far forward. Screw the die in a little and try again. Repeat until the case chambers as a crush fit and then keep on going turning the die in by tiny amounts until you just get completely friction free chambering. Lock the ring there and resize a lot of cases ensuring they all chamber freely. The shoulder should now be just a thou' or two shy of the front of the chamber. Sometimes this position is where you started with the die in hard contact, sometimes you can see serious amounts of daylight between the die body and shellholder. You have to disassemble the bolt to be able to feel any resistance caused by a tight case to chamber fit, and the idea is for the bolt handle to virtually drop closed under its own weight. Hold the bolt handle / knob gingerly between thumb and fingertip and don't push down at all as there is a lot of camming power.
You get the same results quicker but more expensively measuring fired cases using callipers and a Hornady L-N-L comparator body and case headspace gauge. Measure several fired case head to shoulder datum point distances and set the die up to produce cases a thou' or two less for target / pest rifles, maybe a little more for larger game rifles that must function reliably in every condition.