f) Not enough information provided.
For one, it'd be nice to know where you're located! If you get funded for 350K, that in itself says nothing if we don't know the current and projected monthly operating expenses as well as the scale of any (hypothetical) revenue your start-up might generate with that investment.
Let me first start by saying that if cash weren't a constraint, you should choose c) because a) and b) will get you outsourced garbage (see this: Dilemma: to outsource the coding or do it yourself) d) is risky because you're giving out a title upfront, and even if the person could be a true CTO caliber, you should never ever commit to long anything long-term for big titles until the person is proven to able to perform in YOUR start-up (the CTO of BigCorp Inc. might not be start-up CTO material!!) while with answer e) mentality you will stay at the start-up stage forever. The goal is to build and grow a business so that you stop being a start-up. When you hire people, start first with a trial period! By hiring people, you're creating opportunities: may be you hire an iOS developer and a C# or Java developer and 6 months later, BECAUSE you had these developers with you, you will think of something new/better/different that'll enable your start-up to succeed. So short story; hire in-house!
Now let's do some hypothetical maths because in reality, cash is always a constraints.
Let's say there are 2 founders (you mention "if we get funded") and that you cost 4K each (high co-founder equity = low salaries + payroll taxes); 8K
Let's say that you're renting a small space and that you're not in New York City or Silicon Valley and that you're also renting servers or some kind of hosting solution: 1K
Let's say that you're projecting a monthly advertising budget for online advertising: 2K
Let's add monthly average miscellaneous expenses: some are recurrent (bills and supplies) while some hit you every so often (travel expenses, lawyer, bookkeeper, accountant...): 5K
Let's add "opportunity expenses" so that if something comes up you have some leeway to spend on without having to redo your budget every month: 3K
Let's add 2 new developers because of course if you're getting funded it's to build a business! So we'll just say 8K per month each. 16K
This all adds up and if you're running a start-up, that's probably what you'll be up against; and if you're below costs, then great!! Total so far: 35K
Now as you know, the life expectancy of a start-up is equal to cash raised / monthly burn rate. And your job is to get the company to be self-sustaining before you reach 0 by creating a monthly revenue stream that covers the monthly expenses. So, 350 / 35 = 10 months. Do you think that with 350K and the assumptions I'm proposing you could build a monthly revenue stream that could bring in 35K per month in 10 months or less? If not, then you would need to lower your burn rate, or figure out a way to generate more revenue by opening different distribution channels. May be you don't hire the two developers and save cash by coding yourself; may be you choose a) or b) and outsource the development for a third of the cost to give yourself more runway; may be you choose d) and hire a CTO for equity and take a risk on someone so that you conserve cash. In any case, make your own assumptions and decisions and have some idea about where you think you're financially heading when you make decisions because every business decision has a financial consequence. BTW, you might have noticed that I'm not including any revenue you might generate during these 10 months; that's because I'm not including another start-up axiom: everything costs twice as much as you think. So in your projections, unaccounted projected revenue should be allocated to unaccounted/unforeseen expenses.
The other way of looking at the issue is to ask yourself if, using the same kind of approach, you could build something worth investing more cash into before you run out of cash? Raise a 2Mio VC round in 12 months for instance?
So with all this in mind YOU MUST be able to look at your budget, MAKE ASSUMPTIONS, and answer this question YOURSELF!!!! Otherwise, savvy investors could think that you just don't know what you're doing. You're not supposed to have the exact or correct answer to that question because it's a question where there's no definite answer anyway: the future is uncertain. However, you should have YOUR answer: you should be able to explain to investors (and employees) why you're making such and such decision and back it up with some sort of financial projection that may or may not turn out accurate as time goes on.
The question is really the question every entrepreneur should have at least a workable answer to: if I decide to do/not do X, given my current and projected monthly burn rate and my current cash position, am I on track to a) building something self-sustaining, b) crashing and burning in =(expenses/cash) months or c) get more funding before I hit the ground.
So, without more information than what you gave us, I don't think anybody can give you a good and relevant answer for your start-up. Hence f)