I am still going to answer the OP's question though
In general I would say Queen rupees, because you only have 4 dates for a basic set - 1862, 1874, 1875 and 1876. With Empress Rupees you have most years 1877 to 1901, although most of the 1890s did not have coins (1890, 91,92, 98,99 did), not so sure about 93 - 97.
That is if you want a BASIC set. It gets harder if you want say one coin of each mint - Usually Kolkata (Calcutta) and Mumbai (Bombay) and then they have mintmark types like recessed dots, raised dots, small B and C in the leaves etc.
If you go to complex and want all the varieties I would collect both types but focus more on the Empress Rupees as they are easier overall and a bit more affordable as varieties go. For instance if you count all the dot varieties (Dots added each year and by hand, so sometimes say 5 dot varieties may be in different places etc) and then add in mints (1862 Rupees you also get Chennai mint (Madras)), and if you go beyond Victoria out to George VI, you will hit the Rupees and other coins minted in Lahore, Pakistan.
I don't think there would be an easy way to get every single minor variety of 1862 rupee, mainly as the coin was frozen date for 12 years.
Examples of 4 and 5 dot, 1862 rupees - likely struck in 1865 and 1866. Dots are above the flower at bottom below date.
Finally you overlook the last group of Victorian Rupees and these are the East India company rupees of 1840. They were too frozen dated in 1840 and minted through at least until 1857/58 when the Raj was declared. These coins did not have dots and the only major change was the placement of the inscription of Victoria Queen, above the middle for early coins and more lower down for later ones. Like later rupees, these coins are very common and minted in the hundreds of millions, quite amazing for the early/mid 1800s.
If you want to venture away from Viccy, this East India type was also issued in 1835 and used with William IV - again a bazillion varieties, but a super common base coin.

Basic 4 types of 1840 - 57 rupee I have, earlier at top, later at bottom.
Good luck whatever you do, its a fascinating aside collection and rupees are fun and affordable, plus with high silver prices, you are getting a high purity silver coin too (Weirdly at .9167 silver).
I love coins. Especially silver, gold and anything really old.
Member of the Royal Numismatic Society of New Zealand and the Auckland Numismatic Society