Let's work backwards. Closings generally take 45-60 days. That means that, if nothing goes wrong, you should apply for financing at the end of May. You might want to build in a bit of a cushion. So now we're at mid-May.
By that point--mid-May--you'll have an accepted offer. Let's work back from there. How long will it take you to search for a house, make an offer, and negotiate? Maybe you'll get lucky and find a house on your first weekend out. Maybe it'll take longer. A lot depends on how particular you are, and how realistic your price range is. But let's say a month. Maybe 3 weeks to look at houses, then you make an offer, get a counter, and accept. That's about a month. So now we're back to mid-April to begin your house hunt.
How long will it take you to find a Realtor? Probably not long, but you should interview at least 3. Allow a week to interview multiple Realtors and make a decision. Now we're back to early April.
Now: How about your finances? How good is your credit? In fact, what's on your credit score? Are there mistakes that have to be fixed? Are there other things--not mistakes--that should be corrected or addressed? Recognize, too, that many/most sellers ask for some sort of pre-approval or pre-qualification with the offer. So you really have to work backwards from mid-April (when you make your offer) to make sure that your finances are in line.
Understand that credit reports aren't corrected instantly. And if there are some things that should be moved around or adjusted (for instance, paying off a few small debts), that'll take a while to ripple through--from your paying them to the creditor receiving them, and then the creditor reporting the payment to the credit bureaus. Allow at least a month for that. And now we're back at mid-March.
So I guess you can take this weekend easy. But you really should get to it soon.
Hope that helps.