I will not 'choose' items; items received from shrines are always randomized. Items found on the grid (in trees, walls, or '?' tiles) have their tiers set, but the specific item randomized, until it hits '0'
I always disliked the idea of randomizing item/relic names AFTER the game has started and only set their tiers, because it can create unfair contrast between player's pickups. The fairest grid creating method IS to determine not only the tier, but the item's name too when you put it on the grid
(it fills you with DETERMINATION), so it doesn't allow anyone to either "luckily" pick up 2+ items that are in good synergy (unless it's intended), an item and a relic that are OP together, continuous useless items or repetitive items, etc.
It would have made sense for example if the 4 hidden Tier 5 items in the middle didn't have 2 Soul Shards, or if the outer radius of the middle item stack contained at least 1 Flammatory Spices. If you don't want to set everything, you can still randomize the items before the game starts, but then lock those randomized item names, tiers and locations once the game started. (After that but before you start the game, you could still use your judgement whether anything needs to be changed. e.g: items that are harder to reach because of walls or traps should be stronger, while ones near the border tiles should always be Tier 1 or rarely 2)
Another thing that I dislike about post-start randomizing is that it makes it harder to rule out host bias, if there is suspicion of it. *cough* RS2 Portal Gun *cough* Anarchy
About the item percentages, I can see why we are getting so much luck lately. The percentages are too high. Instead of 1:1,5:2:2,5:3, I think that a 1:2:3:4:5 ratio would have been a bit smoother. (Tier 5: 6%, Tier 4: 13%, Tier 3: 20%, Tier 2: 27%, Tier 1: 34%)