I've used the V1 and love it.
It was a back-up to my Nikon SB-5000 for a wedding last year.
I was so impressed testing it, I wound up using the V-1 for most of it.
I'll buy another one as soon as I can afford it.

I knew the V1 had a much longer battery life but it gave me more consistent good exposure than the SB-5000, which surprised me, being a Nikon Fan-Boy all these years.
The head also tilts back without having to rotate, which makes it great for bouncing the light.
And..it has a radio receiver to use remotely.
(The Nikon does too, but it's not as easy to use)
With the dome head diffuser, it works great in a softbox or umbrella, filling them more evenly.
And....the V1 is about half the price of Nikon's current top of the line flash.

Re: round highlights...
The round head isn't that much bigger than a standard rectangular head so the difference of the reflection in the eyes may not even be seen.
For portraits, I'd use a modifier like a softbox anyway to smooth the shadows cast by the flash. Size matters! You need a bigger source to soften the light, not just have it be round. Used w/o a modifier, it goes give a smoother transition than say a TT860 or probably a lot of other rectangular flashes. See photo below. V1 on left, 860 on the right as 28mm setting.

Good video review HERE.

I would buy mine from a local store if you still have one or B&H, Adorama (Flashpoint brand), or some other reputable brick and mortar store.

We have our own Portrait section here on the hog:
https://www.uglyhedgehog.com/s-127-1.html

Another good place to start with leaning about lighting is Strobist Lighting 101.
Then you can move into 102 and 103

Neil Van Niekerk has a great site here: https://neilvn.com/tangents/flash-photography-techniques/
Joe McNally is another https://blog.joemcnally.com
FaceBook has several groups, one of which is titled “Portraits and off-camera flash”

If you are in the market for a new Speedlight and are serious about learning and mastering flash technique, I would definitely recommend the ROUND head. I.d go a step furter and select one with a user-changeable flash tube, bar bulb operation when required, and interchangeable reflectors. There are several reasons.

PARABOLIC THEORY: A round reflector is a parabolic type which when combined with the appropriate flash tube and head design will produce more even and a wider beam of ligh than the usual rectangular configuration of most speedlights. The unmodified parabolic reflector is better for feathering and partial bouc where you are using the edge of the beam.

FLASH TUBES: The plugin type of tube which usually accompanies units with interchangeable reflectors emits more light from the sides of the helical shaped (coiled) envelope than from the front ort top of the tube and will produce more lumens-per watt-second than because that light direction will strike the inside of the parabolic reflector and move forward with more effective power. When used without the reflector in the bare-bulb mode it will provide omnidirectionally which can be useful and it will be more effective when used in a softbox. If it is accidentally damaged, it can be easily replaced.

INTERCHANGABILITY: There are reflectors available that can be used directly with wide-angle lenses and provide better coverage or use with normal or longer focal length for more even lighting. With a small tube position extender and a special mirror-like telephoto reflector, you can fill light a subject taken with a very long lens- up to 600mm. I have a specially designed high-output reflector that will add 1-2 more stops to an umbrella rig.

If you want to fill in natural or existing very low ligh with just a wink of flash. bare-bulb will knock 2 stops off of your lowest power setting.
You can still bounce and .or use a wide variety of modifiers that are compatible with round heads.

These heads are available on units made by Lumadyne, Quantum, Norman and thereis a really nice one at a lower price marketed under the brand Flashpoint. There are also a few one-piece hot-shoe mountable Speedlight with the kind of head designs.

This is not to say that the traditional rectangular Speedlights are bad. For their size and price, many of them are remarkable good but the small linear flash tube in a small enclosure with a highly polished reflector will not do the same things and provide the same flexibility as the round ones.

I've been trying to get more information on the AD200 si I can advise. I know it has a round reflector but I can't tell from the pictures if it has a plug-in flash tube or a fixed circular to the helical tube. I know there are modifiers and accessories that fit on to the unit but I haven't seen them in the illustrations as yet.

The reflectors I use on my Lumadyne heads are not all Lumadyne original equipment. Some are originally made for Ascor, Norman Q-Flash heads but they al,l more or less, fit with a slight alteration. This can be done with the Flashpoint model I am suggesting. That unit is moderately priced and operates with a shoulder-carried power pack- it's very powerful.

I use my units, mainly for on and off- camera hand-held shooting of events. For portraiture, I recommend Monolight with modelling lamps.

I've been trying to get more information on the AD200 si I can advise. I know it has a round reflector but I can't tell from the pictures if it has a plug-in flash tube or a fixed circular to the helical tube. I know there are modifiers and accessories that fit on to the unit but I haven't seen them in the illustrations as yet.

The reflectors I use on my Lumadyne heads are not all Lumadyne original equipment. Some are originally made for Ascor, Norman Q-Flash heads but they al,l more or less, fit with a slight alteration. This can be done with the Flashpoint model I am suggesting. That unit is moderately priced and operates with a shoulder-carried power pack- it's very powerful.

I use my units, mainly for on and off- camera hand-held shooting of events. For portraiture, I recommend Monolight with modelling lamps.

The AD200 and AD200Pro come with both a rectangular fresnel head and a bare bulb head. You can also add an accessory round head. I have three AD200PROs and they are so versatile with those head options. I also have V1 (round head) and V860ii which have the rectangular heads. You can get an adapter for the rectangular V860ii to use all round head accessories and modifiers made for the roundhead V1.

The Round heads give off the rounder light spread which is more like the natural shape of sunlight for portraits. The rectangular light spread fits more a wide angle lens angle of view. With modifiers the shape of the modifier will determine the final shape of the light spread. It is personal taste and personal preference what you like.

The bigger monolights all have round heads, so that look is more closely matched with a round headed flashgun.

FYI, I now own one V350s, three AD200Pros, two V1s, one AD300Pro, two AD400Pros, two AD600Pros.

The AD200 and AD200Pro come with both a rectangular fresnel head and a bare bulb head. You can also add an accessory round head. I have three AD200PROs and they are so versatile with those head options. I also have V1 (round head) and V860ii which have the rectangular heads. You can get an adapter for the rectangular V860ii to use all round head accessories and modifiers made for the roundhead V1.

The Round heads give off the rounder light spread which is more like the natural shape of sunlight for portraits. The rectangular light spread fits more a wide angle lens angle of view. With modifiers the shape of the modifier will determine the final shape of the light spread. It is personal taste and personal preference what you like.

The bigger monolights all have round heads, so that look is more closely matched with a round headed flashgun.

FYI, I now own one V350s, three AD200Pros, two V1s, one AD300Pro, two AD400Pros, two AD600Pros.