Being a fully paid up Luddite, and TIGHT, my list would start.
Buy cheap, buy at least twice, for many things.
A cheap Tap broken in a workpiece can be expensive!
But we all have to balance cost against value for money, especially where the tool is likely to be used for only one job. (Odd ball Taps / Dies or gear cutters Don't ask! )
Assuming that you already have a sturdy bench ) a good vice. Costly but worth it. Have seen cast Iron vices broken by using as a press We ALL do it. Record if you can afford it, industrial quality and take a LOT of wearing out!
A 6" Bench grinder (The wheels will almost certainly need dressing to true them to reduce vibration ) Will be invaluable when you want to sharpen drills / grind lathe tools.
Bench Drill press. Cheap ones are barely, if at all, better than a good pistol drill in a matching bench drilling attachment. Was not impressed by a £50 three speed one. That got little use and found a new owner
Buy good quality drills, cheap ones wear out quicker, and may be less accurate than the more expensive makes..
Ditto for Taps and Dies. You are likely to make up quite a variety of types, eventually.
Once you have a lathe, you will never want to be without one! Unless you want to turn tele legs for motor cycles, you may be able to cope quite well with a mini lathe.
They will swing 180 mm and have centre distance of 400 mm. Don't need a lot of bench space, and are extremely useful. Lots of accessories available, when your requirements expand, and moderately priced.
And the change gears allow thread cutting (If you choose so to do instead of using Taps and Dies for sizes up to 12 – 13 mm ) and fine power feeds. Cross feed will need t you to learn how to turn a handwheel slowly and steadily.
Buy from one the normal Model Engineering suppliers, such as Arc EuroTrade, Warco, Chester, Axminster, SPG, etc. In that way you will get service and spares back up if it is needed.
Have to admit to not being a fan of Machine Mart. Never impressed by their back up, but that may have been our local store.
Every machine has its limitations, but it is amazing what can be done by making best use of the features!
You will need measuring equipment. Initially, you could probably cope using a LIDL / ALDI 6"/150 mm digital You can spend a lot more if you wish by buying more professional instruments.vernier, but £10 can be a good starting point.
Eventually you will probably find a need for dial gauges (Plunger and Finger types ) and magnetic stand for them.
Certainly when you fit a 4 jaw indepenent chuck to the lathe. (Holds work that cannot be held accurately in a 3 jaw , or when it needs to be accurately centred )
Hope that all this rambling is of some help
Howard