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Here are a couple investment tips.

First off, investments can be only made in any port that is marked "Allied", or in ports that are territory of the investor's nation.
Second, investments can only be made once per visit to a port. Consecutive investments can only be made by use of Request Investment Book or by visiting another port before returning to said port.
Next, Investments reveal upgrades only you can see! Thats right, investments in home country and other countries reveal upgrades at the Shop Keeper and Craftsman, like new clothes and books, etc.. also, development status is a combined effort of all investors, revealing upgrades for everybody. This is the reason that when you go to seville you can build really nice ships.
Lastly, investing gives you lots of trade fame and the amount you can invest increases each time you invest a certain amount of money (see the table below). You can also get court ranks by investing and a nice book (depending on home city) at 1 million investment!

I would always encourage anyone to invest in the town he or she frequents the most. When you are beginning, there is little reason to invest; but eventually start your investing with 20% of your equity.

Below is the list for all items that acquirable after invest, either rewarded or bought.


City Item(s) Notes

Aden

Perfumery Secrets 500,000
Amsterdam &
London
Arguin 300,000
Beirut
Bergen Approx. 600.000
Bremen Ticket (NO. 1) Approx. 320.000
Calicut 1,500,000
Calvi
Candia 300,000
Copenhagen Approx. 600.000
Dublin
500,000 or top investor

(This might not be true)

Hamburg 600,000
Helder
Jeddah 2,600,000
(Possibly 2.5M)
Lima 2,000,000
Lisbon 60,000
(could be less)
Lubeck You must be top investor

(Note: This book can also be gotten from the Dublin Item Shop at High Investment rank)

Ragusa {{Craftsman's Boot Enhancement}} 1,200,000

Salonika

Benghazi

Merchant Hometown Promotion to Squire 100,000
Saint-Georges Approx 300,000 Investment
Sao Tome 400,000 Investment
Venice E.Mediterranean Cookbook
Zanzibar 2,000,000


Another type of "reward" for investing is the ability to buy additional items from various merchants.  I will attempt to start a table identifying those items below, and hope that others will contribute. 

For investment Cookbooks, see http://unchartedwaters.wikia.com/wiki/Category:Cook_Books#Bought_or_Investment

City Merchant Investment amount item(s) available
Abidjan Market Keeper diamond
Ambon Market Keeper dorian, Java calico
Athens Market Keeper oak moss
Beirut Market Keeper Sword of Damascus
Benghazi Market Keeper myrrh
Bordeaux Market Keeper bergamot
Calais Market Keeper ~$300K gobelin tapestries
Calicut Market Keeper sapphire, sandalwood, black tea
Cape Town Market Keeper diamond
Caracas Market Keeper opal, sisal, cacao, glass
Ceylon Market Keeper 60,000 ruby, sapphire
Danzig Market Keeper amber
Edinburgh Market Keeper flannel
Faro Market Keeper ~40,000 sherry
Genoa Market Keeper velvet
Grand Cayman Market Keeper flannel
Hormuz Market Keeper turquoise, lapis lazuli
Jaffa Market Keeper narcissus
Kolkata Market Keeper ruby
Luanda Market Keeper diamond
Makassar Market Keeper tortoiseshell
Malaga Market Keeper sherry
Malindi Market Keeper size kaku
Merida Market Keeper opal
Mozambique Market Keeper tea
Nantes Market Keeper 120,000 fennel
Natal Market Keeper platinum
Pegu Market Keeper jade, tortoiseshell, ruby
Pinjarra Market Keeper pink diamond
Pisa Market Keeper velvet
Portobelo Market Keeper chicle
Riga Market Keeper feathers
Saint Georges Market Keeper diamond
Salonika Market Keeper oakmoss
Sevastopol Market Keeper meadow saffron
Seville Market Keeper muskets
Sierra Leone Market Keeper diamond
Socotra Market Keeper frankincense
Trujillo Market Keeper muskets
Vera Cruz Market Keeper mayanburu
Willemstad Market Keeper tobacco, Dutch chintz

Here is a table to show the progress of maximum investment amounts, to show how many Request Investment Book to bring with you if you need to meet an investment target.

Investment number Amount Total
1 60,000 60,000
2 60,000 120,000
3 60,000 180,000
4 60,000 240,000
5 80,000 320,000
6 80,000 400,000
7 100,000 500,000
8 100,000 600,000
9 120,000 720,000
10 120,000 840,000
11 140,000 980,000
12 140,000 1,120,000
13 160,000 1,280,000
14 180,000 1,460,000
15 200,000 1,660,000
16 220,000 1,880,000
17 240,000 2,120,000
18 260,000 2,380,000
19 280,000 2,660,000
20