Buy a decent set of lockring pliers (not a stamped steel tool). Hozan type are what you want. If you have an angle grinder or bench grinder etc they are extremely easy to make out of an old pair of channel locks.

Makes it much easier to tighten a lock ring.

Also, depending on how anal you are about your frame, you can use the roto lock technique is to install/remove a cog (eliminating the need for a chain whip).

Check your pedals before buying a pedal wrench. Many have allen sockets on the rear or have wide enough flats for a regular open end 15mm.

You do not need much to work on a fixed gear bike.

You will eventually need bottom bracket specific tools. You will eventually need a chain tool.

Spend the money on a good spoke wrench (not the multi size dealys).

Generally speaking, kits will come with stuff you don't need and will contain lesser quality of ools than buying individual items.

All you likely need to get started is a decent set of allen wrenches (not folding, they are a pain to use) and a good spoke wrench. Buy the rest as needed.