Should I always play the same numbers?
You can, or you can change them; the odds remain the same. Since every draw is an independent event and not dependent on any previous draws, no mattery which numbers you play for any given draw, you always have the same odds
Do I have a better chance of winning if I have the correct equity to play?
No, your odds are always the same as long as you are picking x numbers out of a pool of y numbers. The difference is that you get more value from your ticket when you have the correct jackpot size.
Should I pick the numbers myself or let the computer pick?
Any number combination has the same probability of winning as any other. However, humans tend to follow the same trends as one another when making a selection. For example, a human would rarely pick 4 numbers lower than 10 in a 49 number pool, even though it is just as likely that those 4 numbers will be picked as any other numbers. A computer might pick those 4 numbers. Also, humans all tend to use lucky numbers (for example: 7 or 10), which leads to more similar ticket. Using the computer does not explicitly improve your odds of winning the jackpot, but it does improve your odds of being the solo winner if you were to win the jackpot.