The Visitor (standard) Visa is issued for a period of 6 months and is multiple entry.
For your question about trying to get a longer-term visitor visa, like 1 or 2 years, these are difficult to get unless you have been using UK visas for a long time. They prefer the person build up a track record of performance with the 6 month visa. If you apply for a 1 or 2 year visa without such a track record, most of the time they will issue a 6 month visa and keep the difference you paid (which is better than an outright refusal). However, your case may be different and there's nothing at all to stop you from trying for a 1 or 2 year visitor visa.
For your question about flight and hotel confirmations... These do not indicate your sincerity or intention to return to the USA. Their guidance points this out, and sending flight and hotel confirmations simply means to them that you have not read the guidance and possibly do not understand the rules (a bad thing).
Finally Finally, your green card is helpful only to the extent that it demonstrates you have cleared some difficult hurdles in the USA and have (presumably) established a life thereestablished a life there.
To get started, go to Apply for a UK visa