The main funding source I see for startups is either angel investors or VCs. Should an organic growth model be considered for my startup? What are the pros/cons of organic growth?
You should definitely consider organic growth if that is possible for your business.
As James and Alex mentioned, it depends quite a bit on the type of startup you're doing. Anything in biotech, energy, or healthcare will almost certainly need outside funding.
In consumer focused software where the business model is advertising based you're probably going to need to be looking at outside funding as well. It takes a lot of pageviews these days to buy a 6 pack of Ramen.
For enterprise software, well, that's a different story. Few VCs will touch a niche play since it doesn't fit with their model. If you're chasing a $10 billion market then VC financing makes sense. Angels are generally more flexible here.
But here's the real answer. Do any of these describe you?
If so then you may be in a good position to raise money now but it will be a long hard slog.
If not, it will be an even longer and harder slog. In fact you could probably go on for years pitching potential investors without so much as a nibble. Be warned, however -- no VC will ever tell you no, just that they'd like to see some milestone achieved first. This milestone may change the next time you talk to them. (Disclaimer: I have not tried to raise money for my startup so I'm not speaking from experience here. This is based purely on the stories of many entrepreneurs and VCs that I've talked to over the years)
So if you're in the software business and want to raise money but the first two points don't apply to you, do whatever you can to get to a functional product with paying customers.
Also, Dharmesh would tell you (and I'd agree wholeheartedly) to consider what you want the endgame to be. Do you want a 1% chance to be filthy, ridiculously rich or a 30% chance to be pretty well off and never need to work again. Raising money from a VC will require you to go for the spectacular homerun $200M exit. If you grow organically instead, you can sell out for $20M and still do pretty well.
There are a lot more companies out there that can afford to buy you for $20M than for $200M.
Growing your company organically (or bootstrapping as people tend to call it) can be a great way to grow a business. 37signals are big proponents of this model, they used revenue from consulting to fund building Basecamp and then once Basecamp took off they stopped working with clients and focused on their products.
I have been taking the mostly bootstrapped model. I worked for a year while consulting full-time and over the last year have done less and less consulting as I focus more and more on my business. In the end I have still ended up investing a decent portion of my own money to keep things going and paying my personal bills. I think its a myth that you can start a company with no investment, what people really mean is no outside investment. You will be spending your own time and money on this company.
Of course this model only works for products where you plan on making money early on, my business was profitable from Day 1 and made money from Day 1. If you have a very long ramp-up time or if you plan on building up a large audience and then figure out how to monetize it then it's almost impossible to go this route.
It depends entirely on what you want.
Do you want a nice lifestyle business that turns over a few million a year, or do you want to be the next google? If its the latter you'll need funding, if its the former you won't be able to get it.
Both are hard work, both are entirely okay, its just a personal decision for your founders.
I run company without external investments 4 years. Now we have 20 people on board and full freedom of choice. Venture capital has own rules (I don't like them). However you can't speed up process without investments, so if you really think that 2-3 years is a huge delay, VC should be considered.
Organic growth should be your default model for financing. Fewer than 10% of startups receive financing outside of friends and family. Virtually all startups are bootstrapped.
If your sector is capital-intensive, such as in manufacturing or biotech, you may not have a choice but to seek financing. This is the exception rather than the rule.