I cannot emphasize this enough: get a factory service manual. Yes, you can download it and that might work at first, but buy it. The one you buy will have the correct wiring diagram for your bike, it'll have all the correct procedures for your bike, etc. The one you download may not (later editions add changes at the end for newer models, and those don't seem to make it into the downloadable versions...)

A few things to bear in mind with this manual: Check the updates in the back to see if there's anything specific to your model. Always check this area first, as this will help avoid, say, breaking bolts because you blindly follow the torque specs in the main portion of the manual, when they changed the bolt out and updated the torque spec in the back of the manual. For instance. Not that I've done that.

A list o' stuff I use all the time:

• Rear stand (the SV650 has no center stand, so chain lubes, etc require a rear stand)
• #1 Phillips screwdriver
• needle-nose pliers
• tape measure (with mm marked)
• nice 3/8" drive ratchet
• 3/8" 3" extension
• 3/8" 6" extension
• 1/2" drive ratchet
• 8-19mm sockets (3/8 inch drive); small sockets may be 1/4" drive and require a converter. 6 point sockets are less likely to strip the nut, so the larger sockets should likely be 6 point sockets.
• a 19mm deep socket for the fork caps
• 1/2" sockets in 22mm, 24mm, 30mm sockets (6 point only)
• Suzuki oil filter wrench (cheap! buy it!)
• Small Flashlight
• Small Diagonal cutters
• Sharpie
• small screwdriver set (jeweler's screwdrivers), both slotted and Phillips
• T-handle Allen wrenches (at least 4-6mm)
• 3/8" Allen sockets (4-12mm)
• 5/8" spark plug socket
• magnetic grabber
• Nice tire pressure gauge (the ones with flexible line and a button to bleed air are spectacular!)
• A cheap digital multimeter
• Nice torque wrenches ($$$). Do NOT use a torque wrench in the lower 20% of its range unless you spent an embarrassing amount on it and they explicitly tell you that you can. You'll need to cover the range 7-105 ft/lb. Given the above note, this will likely require 2-3 torque wrenches.
• Cheap Caliper
• Breaker bar
• Assortment of zip ties
• Various pans to catch motorcycle fluids (oil, coolant, etc)
• Nitrile gloves (I suggest against latex; most people will eventually acquire a latex allergy, which isn't fun)

Some more stuff that I use, but only from time to time for particular jobs (or to deal with my screwups)

• Front stand (for replacing the front tire, and fork work)
• #3 Phillips head screwdriver
• A MityVac or speed bleeders for flushing the brake fluid
• Halogen work light
• Vice-grip pliers
• Battery Trickle charger
• Dental scraping tools (good for cleaning goop; buy at an electronics supply shop)
• combo wrenches in a ridiculous assortment of sizes
• Deep socket sets in the larger side of the above range. 6 point only!
• Nice caliper for testing the chain length ($$$)
• Electric impact wrench (for removing the front sprocket)
• 32mm impact socket (front sprocket)
• An assortment of special Suzuki tools that you'll uncover when you read through a particular task in the manual. ($$$)
• Dremel tool (or equivalent) with grinding wheels
• Electric drill with an assortment of bits
• Metric taps (gah! gah!)
• A nice chain tool (for replacing the chain)
• A metal working chisel (for replacing the chain)
• Fork oil gauge (fork work)
• Fork seal drivers (fork work)
• Feeler gauge (for engine work)
• Soldering iron
• Some way of unloading the rear swingarm for rear shock work (I use two sawhorses, a 2x4 and a ratcheting tow-strap)
• Some device that can be used to balance carburetors

You'll also need a huge variety of effectively disposable seals, crush washers, pins, filters, etc. You should determine what jobs you expect to do, and then place a big order through a discount parts warehouse. For small orders, local dealerships are the way to go, but for big orders you can save money by ordering online. When you order from dealerships, find the part numbers in advance and order by part number, or you'll get the wrong part about 25% of the time.

Remember that most of the frame and engine fasteners are steel and the threads are aluminum, so it is very very important not to use too much force. It is very common to strip the oil drain and spark plug threads, and both are a pain in the ass to fix. For both, you only need to apply enough force to deform the crush washer!
Good luck!