Looking for lens

Looking for lens
Camera: Sony A7C II — I recently purchased the body and am now looking for my first lens.
Budget: Flexible. I’d prefer to stay reasonably priced, but I’m willing to spend more if there is a significant benefit in image/video quality, versatility, portability, or long-term value. I’d rather buy one good lens that I’ll continue using than buy something cheap and immediately want to replace it.
Country: United States
Condition: Prefer new, but I would consider used/open-box/refurbished if the savings are worthwhile and it is from a reputable seller.
Mount: Sony E-mount / full-frame FE
Intended use: Hybrid shooting — both photography and video.
If photography; what style: Family photos, travel, portraits, landscapes, street/travel photography, important events, gatherings, indoor photos, and general everyday memories. I’m not planning on doing professional sports or wildlife photography.
If video; what style: Family videos, travel videos, events, everyday memories, handheld video, and vlogging/self-recording.
What features do you absolutely need:
• Good photo and video quality
• Reliable autofocus that works well with the A7C II
• Small and lightweight enough to keep the A7C II portable
• Good for handheld video and vlogging
• Wide enough for self-recording without having to hold the camera extremely far away
• Useful focal range for everyday/travel photography
• Good low-light performance for indoor events and nighttime use
• Comfortable enough to hold at arm’s length while recording
• Full-frame compatibility
• Something that takes advantage of the A7C II without making the overall setup unnecessarily large
What features would be nice to have:
• Compact or pancake-style design
• Relatively bright aperture
• Good background separation for portraits
• Minimal focus breathing for video
• Quiet autofocus
• Weather sealing
• Good close-focusing ability
• Stabilization would be a bonus, although I know the A7C II already has IBIS
• One lens that can handle the majority of my needs without constantly changing lenses
• Something I can keep for many years even if I eventually add more lenses
Portability: This is one of my biggest priorities. One of the main reasons I purchased the A7C II was to have full-frame quality in a relatively compact package.
I want something I can comfortably carry in a small bag or shoulder bag for several hours while traveling. I also want to be able to hold the camera at arm’s length for vlogging without the lens making the setup excessively front-heavy.
I’m willing to sacrifice some zoom range or aperture if it results in a significantly smaller and lighter setup.
Lenses I’m considering:
• Sony FE 28-60mm f/4-5.6: I really like how small and lightweight it is. The size seems almost perfect for the A7C II, but I’m wondering whether 28mm is wide enough for vlogging and whether the slower aperture will become limiting indoors or at night.
• Sony FE 24-50mm f/2.8 G: Seems like a very appealing balance between size, image quality, aperture, and versatility. I’m wondering if it is worth the extra cost and size compared with the 28-60mm.
• Sony FE 20-70mm f/4 G: I like the extremely useful focal range, especially 20mm for vlogging and travel, but I’m concerned about the size and whether it defeats the purpose of buying the compact A7C II.
• I’m also open to Sigma, Tamron, Samyang, Sony primes, or anything else that makes sense.
Lenses you already have: None. This will be my first lens for the A7C II.
Notes: I’m not a professional photographer or videographer and don’t intend to become one. I purchased the A7C II primarily to capture my family, travel, important events, everyday life, and memories at much better quality than my phone.
I specifically chose the A7C II because I wanted something powerful and future-proof without carrying around a huge camera setup.
Because of that, I really don’t want to put a huge lens on it unless there is a very good reason to.
I’d prefer a compact, versatile lens that makes me actually want to bring the camera everywhere rather than leaving it at home because the setup is too bulky.
At the same time, I don’t want to sacrifice so much image quality or low-light performance that I regret choosing the smaller lens.
My biggest priorities are portability, versatility, photo/video quality, autofocus, low-light performance, vlogging capability, and long-term value.
If you could only buy one lens for the Sony A7C II for travel, family, everyday photography, video, and occasional vlogging, what would you choose?
I’d also appreciate recommendations separated into:
1. Best overall lens
2. Best compact lens
3. Best value lens
4. Best lens specifically for travel/vlogging
Thanks in advance!