Hi OP,
Thank you for the courage to post. It can be daunting. I don't think it's a bad idea to not put any money down if the monthly payment for the property is well within your comfort zone with 100% financing. Check your local credit unions for 100% financing and 3% down options. You can usually get options with more flexible terms from credit unions and smaller, local banks. I would stay away from FHA loans now that the PMI is permanent. Keep in mind that low/no down payment loans usually have steeper closing costs. Property taxes in Texas tend to be on the high side and you will have to fully fund your escrow account since you will not be putting 20% down. Make sure you are prepared for the upfront cash outlay between closing costs, funding escrow, window treatments, furniture, appliances, decor and the trade off between just throwing anything in a rental and wanting nicer/higher quality items for your home. You should also have anywhere from $1000 to 2% of the purchase price on hand at all times for random repairs. You may get lucky in the beginning but sooner or later something will need to be fixed.
The Fed plans to raise interest rates up to 3 times next year. Give yourself some wiggle room by using mortgage interest rates that are .5% higher than the rates quoted today to determine whether you are within the 28% front end (monthly mortgage payment to monthly income) and 36% back end (total monthly debt to monthly income) ratios. Track home prices that meet your criteria to keep an accurate estimate of what your payments will be. Don't force yourself to buy if you will be better served by staying in your rental an extra year or two. Even if you decide to start a family, you would still have two years before you really need a spare bedroom.
Use the time between now and June to tour Open Houses and get familiar with the housing market. You and your wife will be real estate pros by June. You'll know if a home is listed for too much, if it's a good deal, etc. Figure out what the two of you are willing to compromise about (if anything)- yard, nice kitchen, garage, etc. Track how long it takes homes to go pending. Do they sell for less than list price/list price/or more than list price. Above everything else, make the process as fun as possible.