1.5k is a very low budget so don't expect it will provide you a lot of performance improvements over your old laptop (is it i7 3630QM + GT750M 2GB GDDR5 version?)

What games you wish to play? Dota 2, CS:GO? Or triple A titles?

And BTW don't include monitor in your 1.5k budget, allocate another small amount of money for it.

i7 3630QM is a quad core octa thread mobile CPU while the cheapest desktop equivalent (in terms of core/thread) is i7 which will cost you 1.5k (yes it will take all your available budget).

1.5k can only get you this,

Intel Core i3 6100 - RM 496
Gigabyte H110M-DS2 (D4) - RM 289
Corsair 8GB DDR4 2133MHz Value RAM - RM 168
WD Blue 1TB HDD - RM 215
FSP Hexa+ 550W - RM 188
Bitfenix Nova - RM 149

Total: RM 1505 (ETech price inclusive of GST)

No dedicated GPU so you need to rely on the iGPU for the time being, the performance is almost equivalent to GT740/R7 250, get a more powerful GPU next time when you have more money, the PSU should be able to support it provided you aren't going for the most high end GPU.

A lot of missing/wrong information listed.

There is no G320 CPU, no H81M G1 gaming mobo, no FSP Hexa 650 PSU in the market and an unknown model of Asus GTX750Ti (1GB or 2GB?)

If you mean G3250 CPU then take note that it is last gen hardware (some people will mind, so just FYI),  it is a pure dual core CPU (w/o HT), so this is a very huge downgrade from your current laptop.

If you run Dota 2/CS:GO with this specs, then you can expect to run at fairly high settings, for triple A titles, this dual core CPU might cause some issues.

As for price, it is slightly expensive than the previously suggested build but it comes with a dedicated GPU.

For your current situation, yes I recommend to go for Skylake i3 and use the iGPU for casual gaming for the time being and add a more powerful GPU later when you have money for it.

Running triple A titles with GTX750Ti is not really ideal as the frame rate it can produce is not so encouraging even with the all the settings on low, but your choice, if you are ok with this then go ahead.