In Tanktastic, tanks are unlocked by reaching the appropriate level, then purchased with either silver (normal currency, earned in matches) or gold (premium currency, bought with iap or earned at level up)
Here is a list of good starter tanks:
...etc. Most of these tanks do not cost very much but it might take a little time to scrape up enough coins. Be patient.
Tips for using Beginner tanks
Since your tank will be pretty much stock, you will have to play as a support tank. Once you upgrade it you can (only with some of them) move up to an attacking tank. As a rule of thumb, If you like the tank you got, and you use it often, invest a little in upgrades before you buy another tank. Being able to earn more gold with what you got can be even more valueable than just buying the next tank.
M26 Pershing - Starter's tank. The M26 is a deathtrap at stock level, but once maxed out, it can become a more dangerous tank using it's mobility to perform the fearsome "circle of death". Make no mistake, the M26 is not capable of fighting it out in a face-to-face match with any other vehicle in the game. But, learn to use the fairly high top speed to your advantage, and the M26 can be effective in low-level matches. The max level is 8.
M48 Patton - The M48 is a good tank, but can be easily taken down by any adversary in stock form. Firepower is not particularly heavy considering the tank's level, but the M48 is HEAT-compatible and so damage is effectively doubled. The M48 is an excellent tank for defending the flag in CTF matches, and for forming part of the main battle line in an assault on an enemy base.
Centurion - Maxes out at level 18, which is one point higher than the M48. Damage is "good" for a low-level tank; unfortunately, the Centurion fires only AP and HE ammunition, so in spite of a maximum damage rating of 94, it actually does less damage than an M48 firing HEAT. The Centurion is a well-balanced tank overall, that doesn't do any one thing outstandingly well but does everything at least fairly well.
FV 214 Conqueror - Fires only AP, APDS, and HE. Heavy armor and good HP for tank at its level, but low top speed and poor agility. Use the Conqueror as a support unit.
T-54 - When stock it has decent armor, damage, and speed, but it has slow turret rotation even after upgrades. Still, don't take the T-54 for granted; it can do a fair amount of damage relatively quick, and has enough armor and HP to absorb a fair amount of hits as well.
Type 59 - A basic tank, with statistics somewhat similar to the M48. It's faster than the Patton but has a lower damage stat and limited shell choices. It can only fire AP and APDS rounds. Fully upgraded, it has higher armor stats than the M48.
Type 60 - A small, double barreled, Japanese tank destroyer. It's fast, as expected, but limited barrel movement makes it vulnerable on the run.
Spahpanzer Sp I.C. - Fast, heavily armed, lightly armored. Spawn, kill, die, repeat. It can one shot most tanks in its tier and reload very quickly, making it a dangerous opponent for light/medium tanks.
Type 61 - High amount of damage for tank's level. Fires only AP and HE, but firepower is still heavy enough to do 100+ damage to most low-level tanks. Otherwise, it's an overall bad tank and rarely ever seen in low level matches.
T95 Medium - A very useful tank to have. Damage is light, and the T95 only fires AP and APDS, but the high speed and good armor help make up for the light firepower. Speed maxes out at 50kph+, making the T95 an effective flag-running tank. Make use of the T95's maneuverability and speed to perform the Circle of Death on large, slow tanks with heavy armor and heavy guns.
T-10 - A very, powerful tank at its level. If you can use it properly, and have it maxed out. The T-10 tops out at level 29, and at that level it has enough firepower to one-shot almost any tank it encounters. Unlike most tanks at this level, the T-10 also has enough armor to be able to withstand two, sometimes three shots from any tank's gun that it meets. This tank is highly recommended.
M42 Duster - One of the most unbalanced tanks in its level. Although it is intended to be an AA, it still deals horrendous amounts of damage against most tanks in its level with its rapid fire attacks. It's speed is also an invaluable asset, as it tops out at 57 km/h, making it the fastest in its tier. However, its armor is light, and it cannot withstand heavy fire, so it is better at taking out isolated enemies instead of attacking entire groups.