You should always choose a free web hosting service with free, reliable telephone and email support.
While no host can offer a 100% guaranteed uptime (think problems out of their control, ie. city power outage), they should provide "just-in-case" measures to limit website and email downtime to a minimal. These measures may include 24/7 server and network monitoring, redundant hardware and network configurations, and onsite backup power supply. While you might not completely understand the technicalities of these, look to see if your free web hosting provider has these listed somewhere on their website. If not, ask them about it.
If you're looking for a free web hosting provider, then you should expect to pay absolutely nothing for all the basic features listed above. You shoudn't have to compromise pricing with banner ads. Any free web hosting providers that forces ads on your website is a no-no.
BANDWIDTH OR DATA TRANSFER
Very often web hosts talk about bandwidth and data transfer as the same entity. However, they are in fact, different. Bandwidth is the amount of data that can be transferred at one time. Data transfer is the actual amount of data transferred.
Think of it this way. If bandwidth were a tunnel, the bigger the tunnel the more cars can pass through it. Data transfer would then be the number of cars allowed to go through the tunnel in a given time period, say a month.
The less bandwidth you have, the slower it takes your website to load, regardless of your visitor's connection type. Visitors will have to wait their turn. The less data transfer you have, the more often you will find your website unavailable because you have reached the maximum amount of data allowed to be transferred.
To determine what is sufficient, you need to take into consideration the size of your website and the number of visitors you have in a month's time.
But it doesn't have to be. Let's take a look at some of the most common features a good free web hosting provider should offer:
DISK SPACE AND BANDWIDTH
Disk space refers to the amount of storage space assigned to you by the free web hosting provider. If this is your first website and you have limited or no scripting experience, then look for a free web hosting provider that offers a free website creating application where you can create your website simply by choosing a template and adding in your own text and images.