So,
looking for:
1 EDC. Looking to stay under $100.
There is no need what so ever to get even close to that money, unless you really want to, or have a very good reason for it. Plenty of very good lights for a lot less money.
Primary use is inside vacant buildings & occasional use outdoors (prefer wider throw than skinny beam).
Sadly there is not really any such thing as "wider throw". You can get throw, a beam aimed for distance more so, or you can get flood.
Tube lights as a rule are all floody, this is because they are physically small. And you need a large reflector to get lots of throw, so it just doesn't happen with lights like this. There are optics which can focus the beam, but that's a different thing altogether.
The LED you select will also have a bearing on this. Large LED's like XM-L2 or XP-L's will have a large unfocused hot spot and a bright spill beam. But their range can be quite limiting outside. An XP-G2 or even a Nichia219 LED are smaller and will offer a tighter focused, brighter beam. The spill won't be as bright and by raw numbers they will be lower lumen levels, but they will light up things further off slightly better.
If you plan to use the light outside or in large rooms in vacant buildings, then you may want to consider either an XP-G2 LED or a slightly bigger reflector. They should still be floody enough and will be miles away from a pencil beam, but might be more versatile if you are using them at ranges greater than 20-30 feet away.
I can give you can example. This is a Lumintop 18650 tube light. It has a cool white XM-L2 LED and makes a claimed 900 or so lumens.
Not how the beam is very wide and that it lights up the window on the right of the photo quite well:
This is another tube light of about the same size. It's running an XP-G2 and probably makes more like 600 lumens. Note how the beam isn't as wide overall and the window on the right isn't lit up as well. But also not how much more light is making it to the chimney.
The MH20, SC63 & TK09 seem to keep popping up as suggestions. I'm thinking an 18650, but open to other suggestions.
18650 is the way to go IMO. But it really depends on what you want as a total package. But the 18650 format is pretty ideal IMO.
Another poster mentioned the Convoy S2+, which I'd also recommend. They are $15-20 to buy from places like Banggood, although will take 2-4 weeks shipping. But you can also buy them in the US from places like Mnt Electronics.
The build quality is first class, despite the low price and the performance is brilliant. They use constant current drivers, so no PWM to worry about. And you can buy them in a choice of driver outputs and LED tints. They are all however XM-L2, so quite floody.
The beam from them looks like this:
Tbh they would probably fit your criteria for EDC or as a backup light in a car.
The only real limiting feature of the Convoy S2+, is it only has 3 brightness outputs and no moon light. If you fancy modding this is easy to solve for about $4.50, but that isn't for everyone. If moonlight isn't required, then it's less of an issue. The UI is also a simple click through one, so only one tail cap switch and nothing fancy. Again for EDC you might find you prefer smarter UI's that allow access to different modes from off.
A step up from the Convoy would be the Astrolux S1, also available at Banggood. This was originally a group buy light called the BLF A6 and was created by a group of enthusiasts on a flashlight forum. Physically it's about the same size as the Convoy, but it uses an XP-L emitter and direct thermal path copper board, this means it can run hotter for longer without damage.
It also has an advanced driver, that allows very high output. Basically as high as your batteries can allow, 1200 lumens+. The driver also has lots of modes and you can advance forwards and backwards through them, including a low output moonlight and auto step down from turbo.
It essentially does everything the Convoy does, but takes it up a step and generally outperforms most of the premium brands too.
Sorry don't have a good picture of it, it's the 3rd one in from the right:
Going back to the issue of throw and beam distance. I like my 18650 tube lights a lot, but in larger areas, such as barns, farm yards and outside, you really notice how limiting their beam profile can be in terms of distance. This may or may not be an issue for you.
But for me I like to go up a size if outside. Something "p60" sized seems about perfect for this. With an XM-L2/XP-L and the larger reflector, they still have plenty of flood ability, but also a bit more range too them. And generally are still fairly pocket friendly, although obviously larger.
Something like a Solarforce L2M and a good p60 from International Outdoor Store, or a Convoy M1 or M2. Or the Eagle Eyes X6.
5 lights to keep around house, glovebox, etc. Wont be used much, so would be fine buying one of those 5 packs or similar that I see on Amazon or gearbest. These could be AA sized or really any battery.
There are several choices here.
First and foremost, you don't want anything with an electronic switch. As there will be continual battery drain.
You could indeed use a Li-ion light for this, as the self discharge is fairly low on them. Something like the Convoy S2+ mentioned above would work for this, or the shorty version with the 18350/16340 battery tube. There are other cheaper lights of a similar style you could also look at, but the Convoy's offer a nice blend of performance, quality and price.
Or you could go for something AA/AAA powered. The choice being Low Self Discharge NiMh like Eneloops or Lithium primaries. The latter having superb stand by longevity.
I would consider what sort of beam you'd want however. If you have a torch in a car you'll either need enough light to maybe change a wheel or mess about under the bonnet/hood. Or need it for walking to somewhere to help you. Runtime might be a key consideration here and a 2AA light or 18650 will have a massive advantage over any 1AA offering in this department.
Honestly for the money and if you are in the USA, then Mini Maglites would seem to fit the bill as well as any other.