Your system can use TB2, TB3, and USB 3.1. With TB2, it would need an adapter, but the high pricing of Thunderbolt accessories of any generation makes it a moot point as it is outside the budget. So, for you, USB 3.1 is the way to go IMO. Plus, as others have noted, which will not matter with a single-disk HDD (and will make minimal difference even with a single-disk SATA SSD.) Most hard drives are still developed around USB-A and include a USB-A to USB-B/micro cable - if you wish to use the drive without an adapter, you will need to purchase a USB-C --> USB-B/Micro# cable, which costs only a few bucks.
IMO, skip the LaCie Porsche and purchase a HGST. I feel they offer a better product often for less money. You can often find the 1TB HGST TravelStar for $60 USD, and can purchase an enclosure for it for as little as $10 USD ($20-30 gets an extremely nice enclosure that uses USB-C on both ends, avoiding the need to buy any adapters/additional cables.)
If you are OK with a 3.5 inch, the HGST UltraStar family is arguably an industry benchmark of performance and reliability. It is fast as crap for a 7200 RPM HDD (175-250 MB/s depending on the interface), proven to be extremely reliable, and sometimes is more cost effective because it has a longer service life (5 year warranty, and 5-10 year service life isn't unreasonable.) The primary downsides are a slight pricing premium and the louder noise that is expected of a 7200 RPM 3.5-inch enterprise class drive. This is arguably a "professional" grade hard drive that is designed to run 24-7 for a half decade+ continuously.
HGST UltraStar 7k6000 2TB
3.5-inch aluminum enclosure (this is a budget model - some higher end models do a better job at reducing noise)
(and a USB-C --> USB-B cable to use without dongle)
If you must have 2.5-inch form factor, it might be worth considering the 1TB WD Black or 1TB HGST TravelStar (both 7200 RPM and both often on sale for under $70 USD). While quieter than the UltraStar and more portable thanks to bus power/smaller form factor, they are not nearly as fast, not as reliable, and not designed for 24-7 use.
HGST TravelStar 1TB
WD Black 1TB
Oyen Digital USB 3.1 Type-C 2.5-inch enclosure (great quality enclosure that works great with HDDs and SSDs - cheaper ones exist but IMO this is worth the money)
If you want a SSD, the SanDisk SSD Plus can be purchased in the 1TB flavor for around $250 - all you would need is a cheap USB 3.1 enclosure that includes a type-C USB cable.