My other car is a MINI!!!!
Depending on turbo choice, and the revs required to meet your goals, many would argue that rods are the only internal mod required for a 'safe' 350bhp.
The limit of the stock valve train is said to be 7800rpm, so if you can reliably and safely achieve your 350bhp before 7800rpm then rods and a well built engine are what you need.
If you like corners and cornering then a baffled sump is a good buy to protect your investment, build the engine well, replacing things like the oil pump and rings that people often don't bother with, and bolt in a good clutch that will cope with the torque you're expecting, and you should be good to go.
Internally, all mine has is forged rifle drilled rods on a tuffty-Built lump and a baffled gated sump, it's the ancillaries that get you the power