It is good practice for your new boss to provide you with an induction. An induction can vary in length depending on how many duties or how much training you'll need to support your employer whilst working for them.
The induction will provide you with any necessary training on how to use specific equipment (hoists, bath lifts, etc) and information on other support such as any dietary needs, any medical information or general support you'll provide in your work.
Unless previously agreed, you should not be expected to pay for any specific training that you are requested to undertake.
There is a good chance that you'll start your new job with a probation period.
A probation period is a set period of time at the beginning of the contract which has slightly different terms and conditions of employment (such as shorter notice periods, limited entitlements, etc). It is often referred to as the trial period and it would typicaly last between 3 and 6 months but can be extended with the agreement of both you and your employer.
Throughout your employment but more commonly during the probation period, you might be requested to have a supervision or meeting to discuss how things are going. These meetings should be 2 way and give you an opportunity to express how you feel things are going and whether you need further training or support for some elements of the role.