1. define your budget and potential for use by distance expected to hunt at, and the kinds of critters you expect to hunt. This will answer your needs for how much quality you must afford for a rifle & scope...Under $500, under $800, under/over $1000.

2. The caliber for use in Texas can be anything from a 30-30 to one of the smaller magnums...but the "Great Average" deer/hog killers run from as mentioned 243 to 30'06. I am not a big fan of the 243 simply to escape recoil, IMO the 243 is more of an experts caliber and as such is indeed capable of success in Texas and elsewhere. I favor the minimum bullet weight of 120gr's @ a minimum of 27-2800 feet per second at the Muzzle for reliable Kill Shots for the Average Hunter. Wallyworld/Academy/Cabellas/BassPro/Gander Mtn priced & quality ammo is sufficient for anything you will ever hunt in 85-90% of North America in the Standard Calibers ...kinda like Regular Gas is used in 90% of the cars & Lt Duty trucks in the US instead of Premium Gas. As far as a good average caliber to use anywhere I'd suggest 7-08, 308, 270 or 30'06 as a place to start, or mebbe one of these will be the last gun you will ever NEED or buy. I think of these as "Little Red Riding Hood" calibers, not too big not to small, not too much recoil for anyone capable of hunting, ammo most always available and always at the cheapest price and good for anything on 4 feet you will want to shoot at anywhere & Reduced Recoil ammo if it is absolutely needed for a pre teen sized shooter.

3. Guns & scopes - heres where your budget speaks volumes, Under $500 choices are somewhat limited but doable, I favor the Ruger American @ around $350+/- and the balance of the bux around $100-$150 Plus the Sales Tax on the whole purchase for a $500+ Total out the Door +/- ammo in a 3x9x40 scope like a Bushnell Banner or Trophy, Sightron SI,or something with a Lifetime Warranty like the Sightron or a Swift Premier Grades in this same price range. Again there are lots of low end choices that are too cheap to be believed for a reason. Gun Mfg'er package deals traditionally are a bad choice 'cause they skimp on the scope's quality IMO.
An Under $800 Budget will get you a good well made Quality Gun or a Scope, but not both, and here IF you can find a clean Used rifle of more exspensive model that may be the way to go & be able to spend more money on a better scope.
At the Under/Over $1000 budget is where you can expect to find both a Good Qaulity gun & Scope at around $6-700 in the gun and the balance of $3-$400 in the scope.
EX: I looked at a nice clean used rifle yesterday in a caliber and brand I really like & respect in a Pawn shop that, if I had had the money available and in hand, I would not thought twice about spending the $1000 asking price with no haggling - which may be a 1st for me - in a New York Micro Second & the quality of the gun screamed for a $800/$1000+ scope, for a $2000+ Sales Tax total priced rig ...do I need it NO - I've got 4 other deer shooters now I don't use enough to justify buying another one, that has taken me 3 years to thin the herd and get down to just those 4, do I want it YES, but am I going to buy it NOT anytime soon. It was Georgous though! in a discontinued caliber I already shoot and am set up to reload for.

4. Budget Formula - I used to use a 2/3rd's Gun & 1/3rd Scope budget formula but with todays better quality low price guns you can afford to spend more on better Scopes & get the same results in accuracy. Shop hard & everywhere.

5. Accuracy and Functionality - Accuracy comes from Practice first, second and third. Yes some guns will prefer different brands & bullet weights & styles, but Practice time at the range is the bottom line key. The Big Box retailers promo ammo choices will have the best possible average bullet for Texas Hunting to start with in Federal, Remington & Winchester. You will need hands on experience to learn the differences YOUR GUN prefers and how that preference works on the targets you decide to hunt.

You didn't learn to drive a car by watching a video or asking other folks questions about what to do when UNTIL you had some behind the wheel experience to relate the answers to. I would like to think that if you practice just a little you can expect to be able to achieve "Minute of Deer" aka a 5 shot group with all 5 rounds hitting the target at under 3"s at 100 yard Hunting distances without any problems. Enough Practice may bring that 5 shot group to under 2"s each and every time you pull the trigger. Getting to being able to put all 5 rounds undr a 1" circle is not critical when hunting at around 100 yards...further out past 2-300 yards it Becomes critical for a clean kill.

TP&W used to say that 80/90+ % of all Deer Killed in Texas every year according to their surveys was done at around 75-100 yards...that may have changed a tad but not much I' sure, and mebbe you could safely add 25-50 yrds to that statement. All the calibers and guns you will have recommended can accomplish that easily...BUT ONLY if YOU do your part behind the trigger in Aiming Accurately.
Have Fun and Good Luck
Ron

Being new, I imagine reloading isn't even considered yet.

My advice would be to see what ammo is readily available in your area and compare that with cost and make your decision.
From what I saw during the last ammo crunch .270 and the various 7mm magnums were always on the shelf. But thats here.
As for cost, .30-30 can be found for around half the cost of other cartidges mentioned meaning you can spend more time practicing for the same $.