Make sure you don't go during spring break for Texas colleges. The park will be packed. Usually the second week in March which kills two weekends. Here is a site with a list of universities and dates.
This question has been asked many, many times here. A good search on this sub should be a very nice start.
My quick list of tips:
The hikes on the desert floor are the warmest and are best done earlier in the day, but March shouldn't be too bad. The Chisos Basin is 5000 feet or thereabouts. The rest of the park is 1000-2000 feet, as I recall.
Try to arrive before the weekend to ensure you get a campsite. I like to arrive on Wednesdays. Most people are travelling a long way and will be arriving later in the day. Leave early. It takes me two hours longer to get there than the mapping software says. You will have to camp at a developed campground so you want to know you can get a site and not have to drive to each of the developed campgrounds which are very far apart.
Take a gallon of water per person for all day long hikes. Minimum. Take salty snacks! You will lose so much salt.
Take the South Rim hike. It's 12-14 miles depending on the route you take and the hike will take most of the day. It's the most memorable thing you can do in the park. Better yet, camp up on the rim and watch the sun go down and come up. Nothing quite like it. Sites can only be reserved 24 hours in advance, are somewhat limited in number and quality and depending on the time of year, can be in high demand.
Camp in the Chisos Basin in the center of the park initially. Most of the cool trail-heads start there and since it is centrally located you can save time and gas by using it as a base camp if you want to drive to other parts of the park.
If you are going to be camping at primitive sites, you need to get permits in advance. Remember that for your planning.
Bring all your food and drink. There is not much in the park and what little there is, costs a bundle.
Fill up your gas tank in Alpine or Marathon. Gas is expensive in the park and your driving around in the park will use what you have up.
Bring an anker portable phone charger. Not a lot of place to charge your phones and will keep your phone charged on long hikes. Makes for a lot more videos and pics. I actually face-time people from the south rim. I get 4 bars up there now. Wild.
Be safe. Big Bend is beautiful and dangerous. People die in the park fairly regularly. This past year a US Army soldier jumped in the Rio Grande to cool off near the hot spring and was pinned underwater against debris and drowned. Another couple took a short trail in the heat and she died from the heat. If you die on a trail, they carry your body out on a mule because vehicles are not allowed to travel off-road in the park.