I don't even think there is a way to ballpark that. How much equity they want or get is going to come from the current value of the startup. Most investors (and rightfully so) put very little value in an idea, and much more value on the people, and how that idea has been executed on so far. Unless you have a stellar track record, it's basically impossible to get private investors to drop money simply on an idea.
Professional investors will always take from 20% to 45% of your company, no matter how much you are trying to raise.
There cannot be any logical discussion about what your valuation should be. It's a market: either you have multiple offers of investment, in which case you play them against one another and pick the best one, or you don't.
That's why it's so important to create a market. Read http://venturehacks.com for details on how to implement that strategy.
Another thing to consider is the matter of equity vs debt financing. Debt can be attractive for a lot of reasons, but it depends on the situation.
Mark Suster's blog is a great place to look for information. Here's his post on raising Angel funding, which touches on equity and debt, in addition to some best practices for raising funding from individuals (rather than institutions) which is what you'll probably want to do.
Angel Funding Advice: http://bit.ly/1QOwDZ
While it's true that this is a hard number to come up with, you certainly are going to have to justify your proposal at some point. Otherwise, as "BigStartups" suggests, nobody is going to invest in you.
Take a look at other businesses in your industry. What metric is used to determine their value? You'll have to look at public companies, or private companies that have had publicly disclosed transactions. If you can't figure it out, just get more and more general (e.g., "CRM companies" -> "SaaS companies" -> "software companies" -> "business services companies") until you have enough data to suggest an answer.
Then it's a matter of projecting that metric (usually earnings, but sometimes sales, or even "eyeballs", for web companies), and calculating an ROI based on the time to reach it. Then, the fun part is discounting for time and for risk. The latter is where the magic happens, since it's awfully hard to quantify the risk, but you can bet it represents a fairly large discount.
So, if you think your company will, based on projected earnings and common industry multiples, be worth $25 million in 5 years, great! If you ask for $250,000 for (let's say) 25% of the company, that values your company at $1 million today. You're telling your investors to expect a 25x return over 5 years. That's a lovely return, but you haven't yet factored in the risk that your return will be zero -- a fairly high probability.
So, you'd have to knock that figure down substantially before any investor would consider looking at your deal. Then you have to decide if you're willing to sell off, say, a majority of your company at far less than you think it should be worth. In a nutshell, that's why seed-round investing is a tough game for entrepreneurs, and why so few investors are playing at that stage.
The strangest thing about fund raising is this ... if you price the round (e.g. don't raise convertible debt) investors expect 20-40% of the company no matter how much money you raise with the sweet spot being 25-33%. So the real question becomes how much can you raise given your progress. If you price your round and expect to raise exactly $250k the deal will likely get done between $750k - $1.25 million pre-money in my experience.
If it is software or a web site, you should be able to get it going with savings, credit cards and friends & family before thinking about a VC or even an angel.
I would take a different approach. Investors will tend to undervalue your idea and overvalue their cash. You will probably overvalue your idea and undervalue their cash. So, I would suggest the following:
Set benchmarks or goals that you and your investors agree are important to business.
Then give up the 50% or even 90% on the condition that as each goal is met, equity is transferred from the angel back to you. This shows "sweat equity" and the more success you achieve, the more of the company you own.
A quick and simple example of goals:
Get a patent
Create a prototype
Establish agreement with OEM
Each one of those could be easily be worth 5% to 10% equity. The investor would probably want a floor on the percentage they own, for example 20%. But this would calm any fears of an investor "owning 90% of zero still being zero." It also give you great incentive to make this work. The harder your work, the more of the company you own. The more success you have the better the investor does. This of course is a very simple example but I hope you get the idea.
Your idea may be the best idea in the world, but without (a) experienced team and (b) proof of the concept, you're not going to be able to raise $250k very easily.
Do you have (a) and (b)? If not, can you GET (a) and (b)? You can offer up 100% of the equity, but without a solid team with start-up experience (from idea to exit) and at least some data that the idea will sell well to the target market, $250k is probably a pipe dream.