TL;DR: For a beginner hobbyist, my default recommendations are the TT350 and/or TT685 for a mirrorless shooter, with the caveat that the TT685 might work better if you have a battery grip to help counterweight it from being top-heavy on-camera, or if you only plan to use the flash off-camera all the time.

Don't get a Yongnuo YN-560 IV. It's a very nice unit for what it does, but it's a single-pin manual flash. It doesn't do TTL (automated power adjustment based on through-the-lens [ttl] metering], or HSS (high-speed sync; the ability to use flash with shutter speeds faster than 1/160s [the a6500's sync speed]). It's designed to be really cheap, and to be used off-camera as a manual light. And it's in the Yongnuo 560/60x system. Which doesn't work with the Yongnuo 622 system. Which doesn't work with the Yongnuo/Canon RT system. And it's not like Yongnuo supports Sony TTL/HSS, or the Sony multi-interface hotshoe.

Godox is a better option. They make for-Sony versions of their TTL/HSS speedlights that use Sony MI feet. They support TTL/HSS. And Godox's 2.4 GHz radio-equipped gear is all in the same triggering system, regardless of whether it's single-pin manual only or TTL/HSS capable. They also make bigger than speedlight lights if lighting eats your brain. And the TTL/HSS support is cross-brand. So, say, you win the lottery and decide full-frame is for wusses and you want to go medium format with a Fuji GFX body; then all you have to rebuy is whatever goes directly on the camera hotshoe; your off-camera Godox lights will still work with Fuji gear (with the possible exception of the 350 mini speedlights), so long as the firmware is upgraded to do that.

The one fly in the ointment is that Godox and Sony have a bug with TTL and off-camera operation, where TTL will underexpose with aperture settings wider than f/4. But on-camera this does not happen.

Which of the 9 models of speedlights Godox makes is going to work best for you depends on your budget and how you plan to use the flash. Four of the models basically come in two versions: a "TT" named version that uses regular AA batteries, and a "V" version that uses a proprietary rechargeable li-ion battery pack that has longer life than a set of AAs. The two versions will be otherwise UI-identical, except the V version won't have an external battery pack port. The "V" versions can drastically simplify battery handling for someone who's an all-day flash shooter (e.g., weddings). All the speedlights have built-in radio transceivers (transmitter+receiver). The models are:

• TT350-S ($85) / V350-S ($160). Mini TTL/HSS speedlight. Small and light enough to balance well on a small mirrorless body. But head only swivels 270º not 360º; lacks a recycle beep, sync port, and external battery pack port. The TT350 only uses 2xAA, and is a stop less powerful than the full-sized speedlights. They only do 16 channels, not 32; and in HSS, minimum power is limited to 1/16 power.
• TT600($60)/TT600S ($65) / V850 II ($140) / [upcoming] V850 III ($?). Single-pin manual-only speedlight. All a flash hotshoe can tell it to do is fire. But off-camera as a radio receiver, it allows for remote group, power, and HSS control. The TT600S grounds properly on an MI hotshoe. The upcoming III uses a different (lower-capacity) battery pack [the one used in the V1], and has a slightly updated UI. Not firmware upgradeable.
• TT685-S ($110) / V860 II ($180). Full-sized TTL/HSS speedlight. The Sony version can also do "smart" optical WL transmit/receive, but is not backwards compatible with older versions of WL. The li-ion battery pack lasts roughly 2.8x as long as a set of 4xAAs in a TT685.
• [upcoming] V860 III-S [$230]. Basically a V1 with a traditional fresnel head.
• V1-S ($260). Round-headed poor man's Profoto A1. :D The round head has a more even fall off and spread than a traditional fresnel head and takes the AD200 round head magnetic modifiers without an adapter. It has an LED lamp, a slide lock, and a head that tilts backwards 30º. It also has a 4-way dpad in the control wheel, a SCAN function to find the least crowded radio channels, and a TCM button (for on-camera use only) to lock a TTL-set power level in M. It's UI for radio transmitter use is easier to use than the TT685/V860 II's. The li-ion battery pack lasts roughly 2x as long as a set of 4xAAs in a TT685.

If you're going to a Godox speedlight off-camera, there are three current models of dedicated transmitters (if you choose not to get both a TT685 and TT350 :), and use the TT350 as your transmitter. All the speedlights can be transmitters, too. But the dedicated transmitters have better range than the 350 mini speedlights

The X2T-S ($65), XPro-S ($70), and (if you're in the US), the Adorama Flashpoint R2 Pro II ($70). The X2T is the only one with a flash hotshoe up top. Pro models are the only ones with TCM (TTL Convert to Manual; TTL locking, where the power level set by TTL is locked into M mode). And only the X2T and R2 Pro II have bluetooth capability so you can use the Godox smartphone app to adjust power by group and fire the flashes remotely. Again, which one you want is up to how you plan to use stuff and your budget.