Jaycar is a good place to get amateur kit and some electronics focused advice (in many of their shops - each being different). They have a number of solid choices that should suit in a wide range of prices. Bunnings also has a good range but avoid the higher powered products for plumbers and wood burning; higher powered irons and heavy soldering wire used on circuit boards usually does not go well.
If you are going to be a regular user a temperature controlled station is worthwhile. Otherwise a 20-25w maximum is recommended because it is easy to ‘fry’ the traces and chips with any more, especially while a novice.
I would not be worrying about ‘a kit’, just ‘kit’ including a soldering iron with a set of different sized tips, thin soldering wire with a rosin core, and a desoldering device be it braided wire or a vacuum (sucker) device.
Battery powered soldering irons are convenient but be careful it has enough power and temperature stability promised on the label.
There are lots of good tutorials on youtube, preferably watched prior to spending money.
The solders recommended are not pure lead. They are an alloy, most commonly 60% tin and 40% lead. They flow well, have good conductivity and mechanical strength. Note that the fumes given off from the heated metal and rosin can be very irritating.
For any project I try to work with good ventilation, EG a fan at the back or side to move the fumes out of the room. Lead in particular can accumulate in the blood stream. Even very small amounts can cause health issues as it is in your system forever. There are alternative lead free solders. However I still rely on the regular 60/40 Sn/Pb solder.
My hobby experience with electronics and soldering/repairing goes back a bit. At least to when TV’s still had valves! Another source of guidance/learning, (which is how I started) is to look around your local area for a like minded hobby group. I had a well experienced amateur radio and electronics enthusiast nearby to learn from. The medium sized TV like transmission tower in the backyard was a hint to the interests.
I’ll second @PhilT suggestion to visit a specialist electronics hobby retailer. I use Jaycar regularly, and have used over the previous 12 months a number of their stores in Qld and NSW. There are others/alternatives depending on where you live.
I mostly use a temperature controlled soldering station. I still have an old low wattage fine tip iron I rarely use and a high powered larger tip for heavier joining work that the TC iron finds taxing. Depending on your ambition and complexity of your projects a single low cost soldering iron as previously suggested, and some basic accessories may be all you need to get started. That’s all I had in the beginning.