Your next step is to refine your definition of "investment property," your goals, and to make sure that you and your partner agree on it. The answers thus far seem to assume, somewhat generally, that you're buying some sort of property that you're going to rent out and hold for awhile. Even if that is your plan, that's too vague. Consider the variables:
Are you more interested in current cash flow or appreciation? Don't say "both." Sure, you can have both, but the type of property, the situation, and how you structure the transaction can dictate whether you maximize your cash flow, maximize your appreciation, or achieve some other goal (such as serving as a tax shelter).
Let me give you an example: If you want to maximize cash flow, you want to keep your payments as low as possible. Now, I'm not advocating putting a huge amount of money down, or, on the other hand, getting some artificially low initial mortgage. There are lots of other ways to achieve maximum cash flow. For instance, have the seller hold a second mortgage structured as a balloon payment...with a long-enough fuse that you don't have to worry. On the other hand, if you want maximum appreciation, then you're looking for absolute value...something well below current comps so that you start off with built-in equity. And to maximize appreciation, you'd probably look in a solid, safe, neighborhood. To maximize cash flow, you might look in slightly dicier neighborhoods, but ones that are great for renting.
Once you decide on this, you'll be able to rule in, or rule out, a lot of options. You and your partner--probably with the help of a Realtor--will be able to identify certain geographic neighborhoods that make the most sense. You'll probably be able to identify whether you're looking for a single-family home, a townhouse, or a condo in a large building.
Notice I haven't mentioned price yet. If you and your partner buy conventionally, you'll be constrained to what you can get as a mortgage. So, you and your partner should know what you qualify for. However, there are many ways to buy "more" property than through traditional mortgages. Owner financing, or the owner holding a second--as I suggested above--is one way. You can gain even more leverage by doing a "sandwich lease option," or by using a land trust. (I've posted the strategy on Trulia a number of times.) Financing can turn a bad deal into a great one. Make sure you're working with a Realtor (or an investor) who knows and understand the ins and outs of financing.
You may also want to consider whether you're interested in short sales or foreclosures. I'm not keen on them. They can be good deals, but many aren't. And they're tedious, involved, and unpredictable.
Then you start making offers. And the strategy is different when you're buying an investment property. Some Realtors understand this. Some don't. When you're buying a house for a personal residence, it's likely that you're emotionally involved. You want that particular house. That's fine. But when you're buying an investment property, all that matters is the numbers. Do the numbers work? Can you buy it cheap enough, and/or with the right type of financing, to achieve your financial goals? If you can't, then you move on.
The traditional mindset of many Realtors is to have as high a success rate as possible. That's perfectly appropriate for a home being bought as a primary residence. But the "success rate"--the number of offers that it takes to accomplish a purchase--may drop off sharply as an investor. That's because you're probably asking for more of a price reduction, or better terms. Remember: Even great baseball players get a hit only 1 in 3 times at bat. A pretty good baseball player is successful at the plate only 1 time in 4. You (and your Realtor) may be facing those same odds, or even steeper ones.
A few comments about the advice below: Ingrid is correct: The property should "pay for itself" or, to be more precise, should have a positive cash flow. And that's true whether your objective is cash flow or appreciation. Don't buy a property that'll cost you hundreds of dollars every month just because you think it's a good candidate for appreciation. No matter how good the appreciation, make sure that the property (after all your expenses) at least breaks even.
However, I disagree with Ingrid that the property should already have tenants. Maybe yes, maybe no. Work the numbers first. And recognize that if the property has tenants, you'll be bound by the existing lease...even if the property should rent for far more.
Several comments advise a legal arrangement with your partner. Good advice, but make sure you two agree on the investment objectives.
Bottom line is: It's all about the numbers. And those numbers are determined by your investment objectives. So, define your objectives. Determine what will be necessary to achieve those objectives. Then take it from there.
Hope that helps.