So daily driver and a bit over 1 HP per cubic inch is more than just some minor mods. It is quite doable but will take work and/or some $$ starting with a 318, IMHO. And understand that for typical daily driver use (tooling around town at low and mid RPM's) AND 300-350 HP, it is gonna take an engine with a decently broad torque band.
But, first things first: budget. Can you give us some idea what your budget is on this project? And if you are picking that 300-350 HP number out of the air, would a real 250 HP be OK? That would change things considerably.
For that 300-350 HP range: I would start with assuming a swap-out of the pistons to raise the compression ratio, since the lower compression of the 318's is the hardest thing to work around for both of your stated uses. It also helps with the low RPM torque, which helps to address the daily driver use without have to rev it up all the time. It will also help with fuel mileage (if that is of any concern). But that is taking apart and re-doing the bottom end and that is some mix of $$ and your time and skills, and so that may or may not be what you want to do.
Then there comes the issue of head breathing, and to get up to the 300-350 range, it is going to take quite a bit more than the stock 318 heads offer without a fair amount of porting, big valves, etc. It again depends on that mix of budget and your time and skills.
So OP, do you have the budget to spend $1330-1500 on a new set of heads? That is the easy, bolt-on way to go (well, easy relative to porting your heads and putting in bigger valves, or doing the same to another set of heads). The breathing available for that amount of $$ is gonna get you to your HP goals with some other bolt-on type mods.
If you do the pistons and the heads, then they need to be coordinated to a fair degree with the cam selection so that you end up with a reasonable parameter called DCR (dynamic compression ratio) that gets you a good torque band (for the daily driver use) and yet is easily tunable and not likely to detonate.
