Period correct cookware is pretty easy to organize.  The single biggest thing to avoid is speckled enamel ware shown below.  Some documentation suggests that it did exist during the time period though it was quite rare and very expensive.  Just about anything made of out cast iron is safe.  Items like dutch ovens, cast iron skillets, and pots are all period correct and no will call you out for branding commonly found on them.  When it comes to cups, plates, and bowls tin is always the safest way to go.  There are many vendors who sell tin ware reasonably.  However stainless steel items are much easier to come by for some people and if allowed to patina or cooked with over a fire, pass as tin to most people.  Mrs. Koepp, one of our civilians, recommends finding pie tins from antique stores and thrift shops.  Many of the older ones are made of tin and also come in stainless steel in shapes fairly common to period correct plate ware.

Eating utensils would be expected to be made of tin, silver, or wood.  Forks were three tine and reproductions are quite cheap while originals can be found at antique stores for about $10-15 each.  Spoons tended to be on the larger size than what most of us have in our drawers now as were the "butter" knives.  Cheap silver plate silverware can be found usually in boxes at antique stores quite affordably and good be a good way to collect your spoons and knives though almost all the forks you'll find are four tine.  Wooden spoons can be found most places quite inexpensively and work fine as long as they are not made of exotic materials like bamboo.

A civilian lady could expect to have some porcelain china ware.  Items from the orient were quite celebrated and desired by most people.  So inexpensive china inspired glassware would be acceptable, as well. Tea and coffee were consumed by just about everyone.

Pitchers and wash basins were very common and could be found in many varieties.  With no running water the pitcher and basin was your bath.  When looking to purchase one, a good rule of thumb is to look for ones with less color and design.

Any student of the Civil War is all to familiar with this photo but for new civilians it has a wealth of information.  First you see a camp follower or washer woman and all her camp accouterments.  The man appears to be holding a butchering saw.  For the civilian you'll notice many great period correct items that can be replicated in your camp persona.

1. 2 pitchers.  One glass one appearing silver plated likely for drinking or washing.  
2. 2 Tin basins likely for washing since they appear blackened.
3. Enameled tin plates
4. Enameled tin cups and basins
5. wooden stool
6. tin spoon
7. hot coal iron under the stool
8. tin coffee pot on the far right
9. cast iron stove
10. wash tub
11. Large wooden trunk
12. and many more gems upon investigating.

James Townsend and Son is a great vendor for buying tin bowls, basins, and period correct cookware though be careful not to buy Revolutionary War only items.  Studying period photos available easily online can quickly guide you in how best to assemble your camp impression.  

This is a slideshow I'll be working on for a while but these images give a quick look into common types of period correct seating.  Unfortunately, much of the seating seen at reenactments is woefully incorrect for the time period such as wooden folding church or theater seats and the always terrible "mountain man" seat seen below.

For soldiers, the number one seat available was their hat.  The Victorian world did not believe sitting on bare earth to be healthy.  After that, soldiers usually found used ammunition or hardtack crates to sit on.  More common civilian folding stools or chairs or regular dining chairs would pop up only if the army was camped for any length of time.

Some chairs such as the five board bench or the one board bench can be easily made.  Just make sure if you make a bench, that you use cut nails!