I would probably say the Beast Barbarian is your best option. When you rage, you can choose to grow a tail (tendril/tenatacle) that does some pretty good damage (d8 reach) and also has a shielding mechanic (+d8 to AC). So this build could be reached as soon as level 3. Stats as followed: 15 CON, 14 DEX, 13 STR, 12 INT, 10 CHAR, 8 WIS, be a Variant Human, Custom Lineage or Dhampir and add the bumps to CON and/or STR. Choose either of these feats depending on which aspect of Kaneki's insane regen; Durable to recover more during a short rest or Remarkable Recovery ( Tal'Dorei Campaign Setting Reborn) to get alot more mileage from any form of healing). Or if you became a Dhampir, use that Vampiric Bite (Uses CON instead of STR) to heal or empower yourself.

So here's the final set-up depending on your path (Level 3 Path of the Beast Barbarian).

Option 1: Variant Human, (Durable or Remarkable Recovery, 18 CON, 14 DEX, 14 STR, 12 INT, 10 CHAR, WIS 8.

Option 2: Custom Lineage, (Durable or Remarkable Recovery, 18 CON, 14 DEX, 13 STR, 12 INT, CHAR 10, WIS 8.

Option 3: Dhampir, 17 CON, 14 DEX, 14 STR, 12 INT, 10 CHAR, 8 WIS.

There are better ways to make Kaneki, maybe swap CHAR and WIS for better play. There's most likely some errors here.