Properly cleaning a block...
Properly cleaning a block as well as many other components requires several brushes of different shapes and sizes. Consider purchasing a set from a supplier such as Powerhouse Products because it is designed as a package specifically for engines. Don't try to get by with the scrub brush you use to wash the dishes.
If you are like me, then the tools you already own are probably worth more than your entire wardrobe. If so, you probably already have almost everything you need to build your own Chevy race engines. If not, don't worry. Very few specialized tools are actually required, and standard hand tools available from any hardware store will work fine.
You will need a complete set of wrenches and sockets in SAE (Society of Automotive Engineers) sizes. This means the wrenches and sockets are sized in fractions of an inch. Unless you are talking about some odd accessories like the alternator pulley nut, there are no metric nuts or bolts on a small-block Chevy 350.
A long-handle set of combination wrenches is invaluable. A combination wrench has a box end on one side and an open end on the other. Make sure your primary wrenches have nice, long handles, which will allow you to generate plenty of torque.
One or two complete sets of SAE sockets should also be considered mandatory. You can get away with only one set, but having a few different styles will really come in handy. Six-point sockets are hexagonal shaped with six angles. These can put the most force on the head of a bolt without damaging it, and so should be used on hex-head nuts and bolts whenever possible.
But some high-end bolts, which are commonly used in race engines, utilize a 12-point head and are not compatible with six-point sockets. For these you must obviously use a set of 12-point sockets. Also, as a general rule, you want to use shorter sockets whenever possible to reduce the chances of a socket slipping off of a bolt and rounding the edges. Naturally, there are several areas on most motors where a set of deep-well sockets is the only option that will work.
In my opinion, one of the...
In my opinion, one of the greatest things to happen to hand tools in this decade is the ratcheting box-end wrench. I've upgraded all my combination wrenches to these from Gear Wrench, and they are used much more often than my standard wrenches or ratchets.
Of course, sockets are useless without ratchets. Ratchets are sorted by the size of the drive stub, which connects to the socket. The most common sizes are 1/4-, 3/8-, and 1/2-inch drives. The most commonly used are 3/8-inch drives, but it is also nice to have a half-inch drive ratchet and companion sockets because the bigger stub size also means the ratchet will have a longer handle. A longer handle makes it easier to put the torque to the bigger nuts and bolts. You don't necessarily have to replicate each socket style in each drive size. If you are just getting started and money is tight, it is better to invest in a few quality sets of 31/48-inch sockets and use a drive adapter to attach those sockets to your 11/42-inch drive ratchet when you need a little more leverage.
One luxury item that is really nice to have when building engines is a speed handle. Over the course of building a complete engine, you will be installing and removing many, many nuts and bolts. Some, like the rod bolts, you will install and remove several times just during the pre-fitting process. Because of this, a speed handle can significantly reduce your build time.
Other tools you will need include screwdrivers (both standard and Phillips head), a dead-blow hammer, pliers, thread taps, a drill, punches, a scribe, and other various tools, depending upon your specific needs. Every engine build is different, so there is no way to tell you every specific tool you will need, but these will cover the majority of your requirements.

You can have your engine machinist...

You can have your engine machinist install the cam bearings, but this is a task that really should be done after the entire block has been cleaned thoroughly. A cam bearing installation tool should be the only means for installing the bearings because it ensures that the bearings won't be damaged. It is a bit of an investment but will have paid for itself after your second engine build.

Six-point sockets (left) put...

Six-point sockets (left) put the most surface area on the head of a fastener, so they can apply more torque without fear of rounding off the edges or otherwise damaging it. Many ultra-strong fasteners used in race engines use a 12-point head that requires a set of 12-point sockets like you see on the right.

A comprehensive socket set,...

A comprehensive socket set, including a ratchet, extensions, and a universal adaptor that allows you to access hard-to-reach bolts, remains a must-have for every mechanic's toolbox. If you don't already have one, consider adding a speed handle to your tool inventory. It significantly speeds up the pre-fitting process.