All you really need is good antivirus (which I unfortunately cannot recommend to you - I do not know any REALLY good).
Android has its own build in and carefully designed memory management mechanisms. Forcing some apps to close, beside of resulting in unexpected behaviour, does not improve performance.
If app is in background it does not HOLD memory - it simply is in there in case you need it back. Android will kill it as soon as some other app or process will need this memory and killing it before only slows your device when you restart app that normally would still be "in memory".
RAM is not some precious resource that is being waisted when app is "in it" and is not running - RAM is simply a container and having it empty does nothing good (nor bad).
As of the Battery Doctor - this app is not perfect and does not always show real results. Nevertheless it still can be helpful - if you see any of your app draining energy, you should investigate. Well designed and developed apps should not impact your battery life significantly. If any of them is - you should get rid of it and look for an replacement. But as stated before - be careful! Google Play is not iStore - anyone can publish anything without any revision whatsoever. Be extremely cautious with new apps, with few comments and low download counter, that require from you all the privileges they only can. I saw an calculator that required reading my contacts list and clock requiring privilege to make extra-pay phone calls.