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A basic socket set and a drill, maybe a lazy riveter and a 1m bar for stubborn nuts and bolts and a brake pipe flaring tool if you plan to replace pipes, they start at around £15.
I use my battery torque wrench a lot though. 200 Nm is enough for most jobs, starting at around £100.
You need an engine hoist to lift the MX5 body off. This has been done without a hoist by cutting the body in half with an angle grinder, but that is a tough job. You can hire engine hoists for a weekend but they are cheap to buy, maybe a second hand one and put it back on Ebay when you have finished with it.