From your explanation the Sole Trader option is more appropriate and certainly easier to manage. There are many differences but the pertinent and most important ones are as follows.
The main difference in your case would be tax and administration. As a sole trader you would need to do a tax return once a year and if you earned less than £11.5k you wouldn't have to pay any UK tax, assuming you have no other income and are a "standard" tax payer. The current tax allowance is £11.5k although this can change.
Submitting your own tax return is relatively straighforward although you may want to consult an accountant. It is generally easier to run as sole trader versus a Limited Company, ie less paperwork and beaureaucracy.
If you go down the Limited Company route, the company would be liable to pay Corporation Tax on any profits and this process is more complicated and you would probably need an accountant to do that for you, which is likely to cost a few hundred pounds every year. You can do it yourself but the process is not as simple as doing your own income tax return.
Also as a sole trader you can do what you like with any income, you can spend it and treat it as your own wages. You can't do that if you set up a Limited Company as the income is "owned" by the company and so you would need to in effect pay yourself a wage from the company. In other words it's more complex than if you are a sole trader.
The main advantage to a Limited Company is that it is easier to sell the business if you want to at a later date. There is nothing stopping you setting up a Limited Company later on, after beign a sole trader if you want to. They can also be more tax-efficient but this would not be relevant to your case if you are earning relatively small sums, if your income increases then you may want to reconsider.
You can see more information here: https://www.duport.co.uk/company-formation/sole-trader-vs-limited-company.php
(I have been both a sole trader and also set up my own Limited Company)