The cheapest £50 buzzbox that have been around for years will do all of that and more . But they're a fair size, and heavy. They are simple DC transformer, which is why they are so cheap. If you're going to use one, then an inverter will give more power and are smaller/lighter/much nicer to use but are more expensive. The rods are expensive unless you buy them in bulk, but if you do that and don't use them much/store them properly you will be throwing most of them away.
By the way, I've had the leads to do arc welding with my TIG welder for 10 years, and have used them once. That was just to see how well it worked, not for an actual job.
You already know where you can borrow an arc welder IF you ever need one, which makes buying one unnecessary. You would be better off putting this money into a refillable cylinder of CO2/argon and a nice regulator for use with your MIG.