The lease market has completely changed over the past year or two.
Now I advise clients to only look about 30 days out.
Otherwise what is available now will be gone when you are ready in March.
If you have to give 60 days notice at your current place you will likely need to give notice first and then look.
That's just the way the market works now. The best houses rent very very fast. It's not unusual for them to
rent the 1st day on the market if they look good.
In the past it was not uncommon to bargain $50/$100, but these days we are finding if you take time to bargain, the properties will disappear and get rented to someone else. Demand is high and availability is low. Rents have been going up sometimes as much as $200/month. It doesn't mean you can't ask, but when we see people ask. I just rented one today that when I asked the landlord if they would discount $50/month he changed his mind and went up $100 based on how fast they rented another property in the same neighborhood. I also had one recently where the landlord got 3 apps on the same day and went back to all the tenants to see what they wanted to offer....higher deposit, more rent, longer lease etc.
We are also seeing fewer landlords accept pets...I'm guessing less than 20pct will accept now due to the demand....so I think the chances of you taking $200/month off the rent is probably not realistic in today's marketplace.
All that is probably not what you wanted to hear, but it's just the reality of the market these days.
Below you can see a link to homes for rent in Richardson at about $1100/month or less.
Right now there are about 30 rental properties available in the city of Richardson under about $1,500, but 30 days out from your move there may be more of them or fewer.
As frightening as it may be, you may have to give notice before you actually have agreed on a lease at a new place. Apartments may be willing to agree up to 60 days prior to move-in.
Try the link below to see rentals on a map. Just type Richardson under Geography, and slide the maximum price (on right) down to $1,500. You can ignore the ones that are above your limit (although some may be willing to come down on price).