I would leave off the skew for the time being. It is fairly difficult to master, and can be one of the most dangerous as it is all too easy to get a catch and have timber come flying off the lathe.
I would go for spindle gouge & bowl gouge, followed by parting tool.
Invest a bit of time building a sharpening jig too. With the jig you can be sure to keep an identical grind every time. Have a look at Capn. Eddie Castelin's website & youtube channel for his sharpening jig system. A similar set up can be built from timber if you don't have access to welding equipment.
A chuck is not an essential bit of equipment, it just helps make some tasks easier and is a bit more convenient. It's all too easy to want to produce stuff folk can easily recognise from the lathe. I have a box full of honey dippers & candle holders, egg cups etc. in the shed which will never see the light of day. Excellent practice stuff, and if you turn out something decent then all the better.
I do a double ended candle holder which is easily achieved using a simple screw chuck and jam chuck. Simple design, and perfect for practising riding the bevel on your tools.
Those are early examples without inserts. When I turn them now I turn them to take the Ikea glass tealight holders, and use a stop end plumbing fitting at the narrow end to protect the wood from the heat candles give off.
