The biggest negative I can think of to your plan is this: chicks create a LOT of dander. It is a super fine oily dust that permeates all surfaces, including vertical ones. They also can be smelly, though that is far less of a problem, especially if you put them on fermented feed. I have asthma and have vowed that aside from the first 24 - 48 hour start up after hatch, I'll never have chicks in my home again. If you have the option of brooding them in your basement, or even in a garage, or can make an outdoor brooder for them which you can provide with electricity, I'd say go for it. The biggest issue might be if you are subject to frequent winter power outages. Also look into this:
https://www.backyardchickens.com/a/yes-you-certainly-can-brood-chicks-outdoors
IMO, heating pad brooding is the only way to go! Your chicks will need a lot of space, IMO, at least 1 s.f./chick for the first couple of weeks, and then 2 s.f. through week 5. By the time they are 5 weeks old they should be fully feathered, and ready for outside temps if they have been properly acclimated, and have a secure draft free area. Again MHP brooding makes it super easy to acclimate them to outside temps.
Other topics for you to consider while doing your homework: Fermented feed, deep litter management in the coop and the run. Building your own coop, or retrofitting a pre-built shed will give you a better coop and more bang for your buck than buying one of the small pre-fab doll house coops. Those are greatly misrepresented, poorly designed, and almost always do not meet the needs of the birds, or the owners. If you are not able to get a "forever coop" built before you need it, think multi-purpose, and build a brooder that can be repurposed as a tractor in the summer months.
Check out Henderson's chicken breeds chart.
For the travel, you can use the HP that you buy for their brooder, along with a converter (12V to AC) that plugs into your cigarette lighter if you want to provide them with extra heat. But, if you keep your car warm enough that you don't need to wear a jacket while traveling, they should be fine in their shipping box until you get them home. After all, when they are shipped from the hatchery, they survive without any extra heat b/c of the box design and the shared body heat. If it were me, I'd do the heating pad. Always good to have one of those converters on hand anyways!