3G in India its actually not that bad at all, if you have 3G coverage. I stayed in some rather remote places and managed to get decent speed rates, sufficient for Skype calls. Also it is inexpensive and often faster then Wifi.
Getting a Sim-Card
can be quite annoying and time-consuming. I never got one in Goa though. Usually you need to fill out forms and give a foto. In India, always have some spare (passport) photos, you probably need them. Indian take their forms very seriously. Requirements always change and might be different depending on the carriers and depending on the state and the political situation.
In Kolkata for example you need to give the number and home adress of a friend, which they will call before activation, in order to verify your details. You need to go to a service centre, fill out forms etc etc. In some States (Mumbai some years ago) you can just buy it in the local shop. 3 years ago in Karnataka it was impossible to get a card activated, it took me several weeks to get a working sim. As you see its a matter of time, so be prepared.
I always use Airtel and Vodafone simultanously and I strongly recommend you do the same. Airtel is the best for Data covrage in the places I go, but it can be a hussle to get the sim. Vodafone is easier to get, but the coverage is not always so great. Both have good and inexpensive Datapacks you can recharge almost everywhere. In Goa you should be fine with both.
VERY important is to take a picture of the datapacks they are selling in the state/city for the carrier you purchase. For example you buy your sim in Mumbai where a 10GB pack for Airtel might cost 352Rupee. Now you go to Kerala were the same pack has a different price, lets say 354Rupee. However to recharge the 10GB pack for your sim, you must recharge exactly the amount from the state you purchased it in, so 352Rupee. If you dont now it, good luck, the Shop-Walla won t know neither (internet might help though). Very complicated, but welcome to India. Before they even had roaming costs when you change the state and some might still do, but it does not apply to data packages as far as I know.
A very good advice is to set your phone (I suppose you will create a Wifi-Hotspot) so that it only uses the 4G/3G Network. Last year in some places phones would rather switch to 2G, even if there was a 3G signal. I don t know why though.
Goa: I have never stayed in Goa, not my cup of tea. But I have heard from quite a few it is possible to rent whole houses in the backside of the beach, and that must be really nice. Goa is very touristy and has after Keralla probably the highest standard for tourist (whatever that means in India). If you want some advice for other places, send me a PM.