You are making the basic mistake of assuming op amps act as perfect devices.
To answer your last Q first:_ Yes you should tie the inputs of unused op amps to stop them oscillating, Off hand I can't remember the recomended way...output to inverting input I think... (I'm sure someone will set me right).
You just are not going to get a massive gain from one op amp.
If you want high gain, spread it over 3 or 4 stages, you will then have a chance to stabilise the dc working point.
If you go for massive gain you are likely to just amplify noise and get the output going hard one way or the other.
Start small and work up, say a gain of 10 in one stage, get that working and add the next stage with gain 10, then a third stage and try with some over all feed back.
You will learn a vast amount by a methodical problem and you will find problems and hopefully solutions which you hadn't even thought off.
Is this an AC signal you are amplifying or DC?

If you really need high gain and bandwidth you will need an instrumentation amp. The LM324 is just a cheapo, solid workhorse (but I still love it )

Your resistor values sound ok (I try to stay below 470k if possible, but have used 2.2 Meg before now) If you are into high gain, you will probably get into decoupling and screening issues too.
Del

Output to inverting input.

Non inverting input to gnd.

For the price of some $4.00 you get, with AD620, an instrumentation amplifier with a gain to up to 1000. Keep in mind that all the internal resistors are laser trimmed for matching ratios, it saves you, even if you want a large quantity. The difference in price between LM324 and AD620 is offset by the price of 0.1% precision resistors, and the overhead. If it is for one or two devices you might even get samples.

Thanks guys. I hope your suggestions help me solve my problem.

I tested the gain for different frequencies of sine wave and it hardly mattered. The gain was same. I did this circuit on an IC trainer kit using patch cords. Would that be a problem in terms of noise in the circuit?

I used split supplies +12V and -12V. But according to datasheet, its compatible with single supply. But, op-amp didn't work with +5V and ground given to supply terminals. What could be the reason?

This isn't a homework by any means.

Inst. amplifier is one of the several stages of my project and the purpose of this stage is to amplify the signal from IR photodiode-Phototransistor sensor which gives o/p in mV. Oh and I'm working on Heart rate monitor.

They are great little op amps and work well on a single rail supply. On a single rail you will need to create a suitable reference voltage (say at half rail) in place of the zero volt reference you had when you used the plus and minus rails.

You didn't say if your amplifier is ac or dc coupled.
BTW. An IC trainer kit will be hopeless for high gain or high frequency work.
Del

You still are not telling us anything useful to let us help you.

I tested the gain for different frequencies of sine wave and it hardly mattered.

That's nice. What frequencies did you test? What amplitudes were the signals?

An IC trainer kit using patch cords will likely not be ideal, but it can be done. A voltage gain of 620 with a 1MHz GBW would expect to have no more than a 1.6kHz response.

Dear friend,

Any where gain and bandwidth product is constant, so i would like know the input signal frequency.

And unused op-amps will cause oscillations in supply voltage only there won't be any effect on gain of the op-amp, so they recommend you to terminate them with appropriate circuit.

The termination can be done in this passion, just make it a voltage follower (i.e feed your out put to inverting terminal and bias the non-inverting terminal with some 1V)

Given the gain bandwidth product of approx 1MHz or less, the maximum frequency at 620 gain will be less than 10kHz. the LM324 data-sheet shows the maximum large signal falling off above 6kHz.

The LM324 is a fairly slow device which is not suited for high gain/high bandwidth applications so bandwidth and peak to peak voltage swing are all critical to your success.