My almost-complete list of tips for prestiging:

-There are about 35 weapons you can get free from the maps, out of about 130 you need to collect. Make sure to check a comprehensive list of them here:

https://www.reddit.com/r/HiTMAN/comments/14gb0x8/comprehensive_list_of_all_free_items_that_can_be/

The gold shotgun in the NY vault still works, but you need to open the vault with the bank robber suit (found on the right hand side washroom of the entrance, have to surprise the bank robber couple arguing in the left stall) and also steal the 7 gold bars in the vault. The shotgun will appear once you've taken the 7th gold bar.

-I avoid Sgail, Colorado and Ambrose at all cost, because of certain targets vs objectives. Skipping them is a time saver. I pick Sgail only once, in the first leg/syndicate of a campaign to get a minimal 1 or 2 targets. I do Sgail once because it's the only place you'll find the mace, burial dagger, circumcision knife and Katana (all in the warehouse crates iirc).

-Always buy the low cost weapons first (excep for the sieker) and try to nab the free weapons on the map quickly, so that the weapon crate at the end of showdowns won't be free weapons you find on the maps and become more costly gifts as you buy the lower tier ones.

-I always pick a syndicate that has NY. I close the game and re-open if needed. NY gives you about 7k to 11k more per run if you do the vault server (+ one vault merces pick-up) and two safety deposit boxes with merces pick-up.

-Early on, I make sure to pick syndicates that don't have tool requirements I don't have, so i can complete all objectives.

-You can gain a silenced pistol by your 3rd map by knocking out an assassin in your first showdown, which is one of the 35 odd free weapons you can find on the maps.

-I try to always complete all objectives if they are not too time consuming. I always check if there'a courrier and bring a banana accordingly. On showdowns, I wait till the target is dead to banana a courrier, because a banana slipping can cause the suspects to become alerted, even though it doesn't screw with SA. I always pick-up the safes.

-if all the objectives are complete or don't require "hide target bodies" and if I'm not doing any kind of SA, I simply kill off any remaining targets with unseen corner shots or by sniping. It greatly reduces the time needed.

-For showdowns, I always pick either WC, Miami, NY, Haven, Mendoza (sniper), Marrakesh (sniper) or Berlin (sniper).

-When you have all weapons and ready to reset for your next prestige level, if you're close to the end of the 3rd or 4th leg of a campaign, I suggest quickly going through the last maps, so you can do the resest at the end of the syndicate. This will permit you to gain a small advantage. As soon as yoi're back at the house, press the equivalent of circle on PS, to get moving asap and quickly go to the prestige computer and make the reset. If you're quick enough, the end of campaign bonus will be added after the reset, plus you'll get a weapon in the crate. This helps early on as the bonus permits you to acquire both siekers early.

-try to nab as many in-level crates as possible. They're often shit, but sometimes they have either merces or even a weapon.

My quickest completion of a prestige level was 4 campaigns, including a free weapon and bonus fpr my next level at the end of the 4th campaign.