Very good. So screen has to be at least 5.5" and you want NFC and something without a heavily skinned UI. Almost all modern phones have fingerprint and 3.5mm jack. NFC can be easily found on mid rage Snapdragon devices and up.
I think its safe to say you have little to no incentive to wait for the Oneplus 6. The 5T has everything you want and copious amounts of RAM. The only improvements the next model brings is greater screen coverage which introduces a camera notch, and an improved version of the already exceedingly powerful SD835 chipset.
If you want something smaller, cheaper, or more robust, you can consider the LG G6. It has IP68 water resistance and is cheaper due to being an older device with the SD821 chipset (which is nothing to scoff at as it is still a flagship tier SoC which is a major upgrade) The screen is 18:9 like the 5T but respectively smaller, at 5.7" diagonally.
Both the 5T and G6 have the same battery capacity 3300mAh and has rear fingerprint, dual rear camera, and NFC. Oneplus devices come with more internal storage but the G6 has a microsd card slot. The 5T has a three position (Normal/DND/Silent) slider as a defining feature of their phones. Both phones at this point have clean, close to stock Android. The 5T is on Oreo and the G6 will get the update by end of June (although in your use case it might not make a difference) The 5T has dual sim slots which makes it more convenient to use if you travel.
For size reference: height x width x thickness
HTC Desire 630 - 146.9 x 70.9 x 8.3 mm, 5.0" 720p screen (66.2% screen-to-body ratio)
LG G6 - 148.9 x 71.9 x 7.9 mm, 5.7" 1440p ultrawide screen (78.6% screen-to-body ratio)
OnePlus 5T - 156.1 x 75.0 x 7.3 mm, 6.0" 1080p ultrawide screen (80.0% screen-to-body ratio)
If you are considering any other phones, do mention and I can make a comparison. The specs of the unreleased Oneplus 6 is inconclusive, although the device dimensions should the same as the 5T, with an enlarged screen of the same vertical (1080p) resolution plus space to the side.
Ok so you don't really need a lot of memory. You don't need much storage, but will you require a microsd card slot? Your 630 has a microsd slot. What about music playback? Do you blast the phone speakers or use headphones/earphones? If you do listen to music, what do you think about the sound quality? For the screen size and overall device size, do you think the 630's screen is small? Are you ok with a large phone (phablet)? Do you travel much and could use two sim card slots?
If there are things about the 630 that really bother you, feel free to sound out so I find a phone that won't give you the same problem. We're almost there.
I don't really use my microsd slot. I usually listen to music with headphones and so I don't need high quality speakers. For the screen size, i would prefer if it was bigger than what it is now, atleast 5.5inch.
One thing I cant stand about my current phone is htc's skin, sense ui is super annoying sometimes, I also don't like that it dosen't have a fingerprint scanner or nfc, although the latter isn't too improtant
So you can get any phone you want that is within your budget I suppose.
What are you currently using? What about it makes you want to get a new phone? What do you like about it? What new features or performance would you want in the new phone? This is so I can look for one that won't disappoint you.
Ok that makes sense as the 630 is a budget device. If you don't need a good camera means you have no reason to sell an organ to get the flagship Apple/Samsung/Pixel devices some inconsiderate people like to recommend here. What about app usage, size preference and how you feel about the battery life of the 630?