I planted a number of the aforementioned varieties this springand all are growing rather well, especially the Triple Crown and Natchez. As a trailing variety the Triple Crown is being trained on a 6 ft. 2 wire trellis. The Natchez will later be on a 3-4 ft trellis but presently is tied on a single 5 ft. stake. I found on a couple sites that the Natchez needs tipping at ~4ft and the laterals dormant pruned to 18 to 24 in. I have done the tipping but now have laterals, some more than 4ft, and they are producing other sets of laterals. I would appreciate suggestions re. how to treat all this new growth -- do I need to pinch the laterals/sub-laterals or just let them grow and wait for the dormant pruning?

On backberries the reason for tipping is to get new shoots that are fruit bearing, as well as some size control. I start tipping at about 36" tall, although a tipped cane will still grow taller from the ground (on mine anyway). I do tip the off shoots when they get long, probably at 24". I'm less vigilant on those. On 2nd year canes I prune back anything excessively long before they bud out in the spring. I posted my experience on raspberries on another post last night. so you can look for that.

Well, that all depends! How long are they, first? You can tip the laterals, which will then also branch...so, you can see how this will increase your fruiting area. However, if your planting is really dense already, I don't think I'd do that. You might end up with too much vegetative growth, which will limit air flow and result in more problems with fungal diseases next year. If you don't thip them, you'll definitely want to prune them back to 12-18" during the growing season. Most growers probably choose this method. Maybe take a small section and tip the laterals, and see which way you like it better next year.

Pruning is done at various times. Your raspberries are both fall bearing cultivars btw. Primocanes are 1st year canes Floricanes are 2nd year canes Fall bearing bear fruit on both primocanes and floricanes. Primocanes will have a fall crop on upper 1/3. The next summer lower 2/3 will fruit (now called floricanes). You can just take the first crop and cut them down. Or you can also take the summer crop. Up to you. If you want both crops once primocanes are done fruiting, cut off upper 1/3, and leave the bottom 2/3's to fruit next summer after winter. So a new cane will fruit in fall, then the next summer will bear fruit again. It is confusing! Some just take one crop to make it easy. I myself take both crops. Blackberries and summer bearing raspberries fruit on 2nd year canes only (floricanes). With blackberries you want to tip them at 4 feet. They will produce lateral shoots, and produce more berries. You can tip them when they reach 4 feet. This is not a set rule, 3 feet or 6 feet, is OK. If left to grow too long berries can break canes from the weight. So best to prune them. New canes come from the crown with blackberries. Just leave them. It doesn't matter how many. Raspberries throw suckers that come up all over. A rule of thumb is to space about 6 inches apart. Any closer it becomes too crowded, not enough light or air flow. Blocking air flow encourages fungal growth. So if new canes are very close, you can thin them out. Do this when dormant. Once floricanes fruit in done, remove them ASAP