It's more involved than what you have mentioned or appear to be allowing to occur in your picture. For starters I think having multiple vertical canes close together is probably a mistake. I suggest you do a search for phrases like "pruning training blackberries" and look for web pages that have pictures showing what needs to be happening. Including the kind of support system that needs to be provided.

Thanks for the comment. My understanding with a semi-erect variety like Triple Crown is I should limit the number of canes to 3 or 4 per plant, and utilize a trellis with an upper and lower wire. Then prune to the tips of the main cain and laterals. My current set up has a wire about 3 feet up and a wire about 5.5 feet up. Does this seem reasonable? If so, then I'm wondering how much pruning to do during this first year.

Maybe you don't want the top level to be so high - what do the directions you've already looked at say?

I did the same set up as you following uga recommendations. Although first year i didn’t cut canes just circled between the two wires. 2nd year the canes will get stout

I have grown Triple Crown for over 20 years. Your young planting is fine, the trellis wire heights are fine. Slender canes tend not to branch on their own, so just let them grow and prune to 10 or 12 feet in October. Succeeding year's stouter canes are typically top-pruned at 5 feet by mid-July, earlier if that big already. Laterals will readily form.

Any laterals started this late in the season will be thin and produce small fruit next year.

Spacing Triple Crown clumps at 3 or 4 feet is manageable long-term, the protocane sprouts tend to stay within a 1-foot radius.

Limiting canes per clump is more a factor of how many berries do you want, and how much wrestling with canes and laterals you want to do. This variety is very productive.

You can prune up to 7 time tip bud first this stop height of plant and start forming laterals doing as pinch bud is easiest to length of 18" this start lateral on limb. This 18" allow you pick all fruit by reaching them. Right this day plant grow more than did all year fall growth is amazing on blackberry plant each limb and lateral grow easy 4" a day lets just take 20 days good growth that comes 80" on each lateral have plant over 14 ft. wide if don't tip. By 18" that gives about 4 days between pruning. You have what called wall berries next year.

Thanks Logician and gator rider. this Is very helpful.