I’ve been a serious cyclist since the 1970s and would NOT recommend a cheap Walmart bike - you’ll be constantly frustrated with repairs, adjustments, things breaking, and schlepping/pedaling a heavy and inefficient bike around. Getting something cheap is false economy, and not fun when you’re depending on it to carry you 10, 20, or more miles.
To a certain point you really get what you pay for with bicycles - once you hit the mid-range of around $1000 it’s diminishing returns when you spend more. For $700 to $1000 you should be getting something that’s reliable, reasonably light, and fairly easy to live with. Bikes do however, require more attention than people think. Carry a spare tube and know how to change a flat, and carry a bicycle multitool to make adjustments as needed. If you’re riding in areas with a lot of goat-heads or other tire hazards it’s a good idea to install “Slime” inner tubes to prevent flats.
There are a lot of frame makers out there, but only a few component makers. A quality frame and fork from Trek, Specialized, GT, or one of the myriad of other quality frame makers with mid-grade to higher-grade components made by Shimano (Deore XT or higher), Sram, or Campagnolo, with a good quality wheelset with Mavic rims is a good starting point for looking.
Shop around, talk to a lot of shop owners about their bikes and the components on them, read a lot of reviews, and be honest with yourself in terms of your needs. You won’t need a super expensive cross-country racing mountain bike to do what you describe. A good quality durable chrome-moly steel or aluminum frame is what you’re looking for in this range. Carbon fiber and titanium are for racing or for those who have more money than sense. You’ll also save money by getting what they call a “hard-tail” bike, meaning that it only has front suspension - not full suspension. Hard tails are generally lighter and more efficient. Full suspension bikes are generally for downhill racing or very fast cross-country racers who are willing to pay upwards of $5K for a very specialized design that’s just as light as a hard-tail.
In terms of security, when I bring a bike it’s on a hitch-mount bike carrier that’s locked to the trailer hitch, and the bike itself is secured to the van’s frame or van’s trailer hitch with a heavy-duty chain and tamper-resistant lock. I’ve never had a problem with this setup.