Now that you have played a few games, are tired of stacks of books and hardboard cutouts, and want to take the next step, I still don’t recommend breaking the bank; let’s look at budget starter terrain.
Most of this terrain will come pre-painted, limiting your upfront time and money investment. This gives you more time for gaming.
My #1 recommendation will always be aquarium terrain.

Rocks, ruins, castles, and plants—all for less than you will spend on two or three paint bottles. Ten or so good pieces will give a very nice-looking 6×4 table with interesting and varied terrain. The biggest con is that aquarium terrain is rarely thematic or scales with the models on the table. (table cost $140)
My following recommendation is to go take a walk. Find some public property along a riverbank or in the woods, grab 10 or 12 interesting rocks/pinecones/logs, and place them on a table. This terrain setup can actually be very thematic and fit your table. (table cost $0)
Another budget item is to visit thrift shops and church stores and look for Christmas village items. This is a great way to get a handful of buildings, perhaps a bridge, and some trees.

The terrain tends to look okay. Your battles can be pretty interesting, and you can even do fun missions, such as escorting Rudolph to the flying sleigh. The biggest downside to Christmas terrain is that it is primarily sealed, and your troops cannot occupy the buildings. (table cost $30-$200)
Trees for Christmas villages could be a category of their own. Often, these are the only trees I use. They look far better than I can make, and they fit the scale wonderfully.
My final recommendation would be to buy model railroad building kits.

Many buildings can be had for $15 or less. You can paint them however you like. They are very accurate to scale if you buy the correct scale. There are endless possibilities. My most significant downside to model railway items is there is a time investment and a hobby side. Most buildings require assembly and painting. The other con is durability. The model railway is for building models that sit and look pretty, not for gaming with frequent movement and other forms of abuse. (table cost $200-$400)
That is just a quick look at the options for terrain on a budget, for a burgeoning wargame. Tune in next time for information on gaming mats and other 2d terrain.